Identifier
-
Mp00030:
Dyck paths
—zeta map⟶
Dyck paths
Mp00229: Dyck paths —Delest-Viennot⟶ Dyck paths
St001929: Dyck paths ⟶ ℤ
Values
[1,0] => [1,0] => [1,0] => 1
[1,0,1,0] => [1,1,0,0] => [1,0,1,0] => 1
[1,1,0,0] => [1,0,1,0] => [1,1,0,0] => 1
[1,0,1,0,1,0] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 1
[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] => [1,1,0,1,0,0] => [1,1,1,0,0,0] => 2
[1,1,0,1,0,0] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 2
[1,1,1,0,0,0] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0] => 4
[1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => 3
[1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 10
[1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 8
[1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0] => 8
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 8
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 6
[1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 8
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 10
[1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0] => 6
[1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0] => 8
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0] => 6
[1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 8
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 10
[1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => 10
[1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 8
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 6
[1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0] => 6
[1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => 6
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 8
[1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 6
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0] => 8
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => 8
[1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 6
[1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 4
[1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 8
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 10
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 9
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 18
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 8
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 13
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 15
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 15
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 10
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 10
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 8
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 19
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 24
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 18
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 19
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 9
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 19
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 8
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 14
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 19
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 19
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 13
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 15
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 15
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 18
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 20
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 15
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 19
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 15
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 15
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 10
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 15
>>> Load all 1200 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 13
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 14
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 13
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 10
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 13
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 19
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 19
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 15
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 18
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 24
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 24
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 18
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 24
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 18
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 19
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 19
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 8
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 8
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 14
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 19
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 19
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 15
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 9
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 13
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 13
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 19
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 19
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 14
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 15
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 18
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 20
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 24
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 18
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 24
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 19
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 19
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 13
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 20
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 18
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 19
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 19
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 15
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 8
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 10
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 15
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 19
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 15
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 8
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 15
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 19
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 15
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 10
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 15
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 19
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 18
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 19
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 15
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 18
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 20
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 15
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 15
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 15
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 15
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 10
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 15
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 19
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 19
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 18
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 15
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 9
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 10
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 9
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 13
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 10
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 9
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 14
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 13
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 10
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 8
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 13
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 14
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 13
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 10
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 8
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 10
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 15
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 12
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 28
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 10
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 19
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 24
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 24
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 15
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 20
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 12
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 33
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 42
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 28
[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] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 41
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 12
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 33
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 10
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 21
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 30
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 30
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 29
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 27
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 38
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 36
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 27
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 41
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 24
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 24
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 15
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 29
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 29
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 32
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 29
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 20
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 15
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 10
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 30
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 44
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 33
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 43
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 42
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 66
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 42
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 28
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 53
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 53
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 54
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 41
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 30
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 12
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 32
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 44
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 33
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 44
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 12
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 30
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 10
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 21
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 32
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 32
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 21
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 32
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 33
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 54
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 44
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 33
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 53
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 30
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 30
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 19
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 40
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 41
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 44
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 43
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 29
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 24
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 24
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 41
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 53
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 41
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 28
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 36
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 53
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 36
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 24
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 44
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 54
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 53
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 41
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 32
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 27
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 38
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 36
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 27
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 43
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 24
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 24
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 15
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 32
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 43
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 44
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 41
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 29
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 27
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 29
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 33
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 40
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 32
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 33
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 40
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 40
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 29
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 30
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 29
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 32
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 29
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 20
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 24
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 19
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 21
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 21
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 19
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 15
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 19
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 30
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 30
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 29
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 33
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 53
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 44
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 33
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 53
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 41
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 44
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 43
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 24
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 28
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 53
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 66
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 66
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 42
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 42
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 53
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 42
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 28
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 53
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 66
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 66
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 53
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 42
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 38
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 44
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 53
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 41
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 44
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 53
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 54
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 41
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 44
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 28
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 30
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 32
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 30
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 10
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 10
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 21
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [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] => 32
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 32
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [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] => 32
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 33
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 53
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 44
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 33
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 53
[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] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 41
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 43
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 44
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 24
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 12
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 21
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 30
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 30
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 29
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 12
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 19
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 19
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 30
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 30
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 21
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 29
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 33
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 40
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 44
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 33
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 53
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 32
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 32
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 21
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 40
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 41
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 43
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 44
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 32
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 24
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 28
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 40
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 54
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 40
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 36
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 42
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 54
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 42
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 28
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 53
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 66
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 66
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 53
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 44
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 33
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 54
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 44
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 33
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 53
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 30
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 30
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 19
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 40
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 54
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 54
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 54
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 40
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 36
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 38
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 36
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 53
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 41
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 42
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 53
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 54
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 41
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 44
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 41
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 44
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 43
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 29
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 36
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 28
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 30
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 32
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 30
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 24
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 10
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 15
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 29
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 43
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 32
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 24
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 41
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 42
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 44
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 29
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 36
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 30
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 30
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 28
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 12
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 24
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 44
[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] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 54
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 43
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 32
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 27
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 41
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 24
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 15
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 29
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 43
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 41
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 44
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 24
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 41
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 44
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 53
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 38
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 42
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 54
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 53
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 41
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 44
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 30
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 28
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 30
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 32
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 10
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 24
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 41
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 53
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 41
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 24
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 36
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 53
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 36
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 24
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 32
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 44
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 41
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 43
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 24
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 27
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 38
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 36
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 27
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 29
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 24
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 24
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 15
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 29
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 44
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 43
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 41
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 32
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 27
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 41
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 42
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 54
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 41
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 36
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 53
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 53
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 38
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 42
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 43
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 44
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 41
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 29
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 36
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 33
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 33
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 33
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 33
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 27
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 12
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 20
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 27
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 33
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 27
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 10
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 29
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 33
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 29
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 20
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 27
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 33
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 33
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 27
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 12
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 32
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 33
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 40
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 29
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 33
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 32
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 29
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 20
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 24
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 32
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 30
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 28
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 30
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 10
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 29
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 33
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 40
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 32
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 33
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 40
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 40
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 29
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 24
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 29
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 32
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 29
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 20
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 24
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 30
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 32
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 30
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 28
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 24
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 12
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 15
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 12
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 19
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 15
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 12
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 21
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 19
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 15
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 12
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 21
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 21
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 19
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 15
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 10
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 19
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 21
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 21
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 19
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 15
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 10
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 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] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 21
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 12
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 26
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 21
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 40
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 15
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 12
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 29
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 43
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 26
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 35
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 35
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 21
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 49
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 35
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 50
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 64
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 40
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 95
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 74
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 16
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 50
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 15
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 12
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 7
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 30
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 47
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 29
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 56
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 51
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 43
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 43
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 26
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 67
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 49
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 74
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 42
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 68
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 56
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 42
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 35
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 35
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 21
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 56
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 78
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 81
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 49
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 54
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 60
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 54
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 35
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 54
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 35
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 51
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 75
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 50
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 110
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 87
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 130
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 72
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 64
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 40
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 102
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 139
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 95
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 109
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 109
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 74
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 113
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 75
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 15
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 54
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 75
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 50
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 111
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 90
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 16
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 51
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 15
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 12
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 29
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 47
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 30
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 56
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 54
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 47
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 47
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 29
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 73
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 82
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 56
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 50
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 95
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 51
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 105
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 68
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 51
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 43
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 43
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 26
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 73
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 102
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 104
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 67
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 75
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 81
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 78
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 49
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 82
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 54
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 68
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 90
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 109
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 109
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 74
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 114
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 82
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 42
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 81
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 106
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 81
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 63
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 106
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 63
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 42
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 87
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 42
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 68
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 56
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 42
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 35
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 35
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 21
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 56
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 87
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 87
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 56
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 69
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 87
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 106
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 117
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 90
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 78
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 81
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 75
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 49
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 85
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 60
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 75
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 60
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 81
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 85
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 69
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 81
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 82
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 85
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 60
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 54
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 60
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 54
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 35
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 60
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 78
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 87
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 81
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 54
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 49
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 56
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 56
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 49
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 35
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 35
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 21
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 43
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 68
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 51
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 95
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 78
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 137
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 75
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 75
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 50
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 111
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 137
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 110
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 113
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 117
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 87
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 113
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 78
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 139
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 174
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 130
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 174
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 139
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 64
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 137
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 72
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 64
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 40
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 95
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 139
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 102
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 109
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 130
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 139
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 137
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 95
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 144
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 109
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 140
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 106
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 137
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 144
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 109
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 109
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 109
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 74
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 114
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 137
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 140
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 113
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 95
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 104
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 102
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 75
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 68
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 43
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 12
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 47
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 72
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 54
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 102
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 87
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 139
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 75
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 75
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 50
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 110
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 137
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 111
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 114
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 117
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 90
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 114
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 81
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 15
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 47
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 68
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 51
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 95
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 81
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 16
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 43
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 15
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 12
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 26
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 43
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 29
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 49
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 51
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 47
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 47
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 30
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 67
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 75
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 56
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 50
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 102
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 54
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 104
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 72
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 54
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 47
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 47
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 29
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 73
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 102
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 102
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 73
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 81
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 82
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 87
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 87
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 56
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 85
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 60
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 40
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 109
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 111
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 137
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 139
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 95
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 144
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 114
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 50
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 102
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 140
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 102
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 75
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 140
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 75
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 50
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 110
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 51
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 105
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 68
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 51
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 43
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 43
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 26
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 67
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 104
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 102
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 73
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 85
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 105
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 144
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 140
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [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] => 105
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 102
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 104
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 102
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 67
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 112
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 85
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 113
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 81
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 117
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 114
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 90
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 106
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 113
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 117
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 87
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 75
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 81
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 78
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 49
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 85
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 109
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 117
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 117
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 82
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 74
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 81
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 87
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 78
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 54
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 56
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 35
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 74
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 109
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 95
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 95
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 68
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 64
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 50
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 102
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 81
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 117
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 114
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 90
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 114
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 87
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 139
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 109
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 137
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 144
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 106
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 109
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 109
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 74
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 113
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 140
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 137
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 114
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 102
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 102
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 102
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 82
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 72
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 47
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 35
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 75
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 113
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 82
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 109
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 130
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 114
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 75
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 74
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 56
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 114
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 144
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 113
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 63
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 109
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 56
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 35
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 87
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 117
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 113
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 87
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 113
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 87
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 42
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 81
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 106
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 81
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 63
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 106
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 63
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 42
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 78
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 42
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 68
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 56
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 42
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 35
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 35
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 21
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 49
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 81
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 78
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 56
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 60
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 90
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 106
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 117
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 87
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 87
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 87
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 82
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 56
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 85
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 90
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 87
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 69
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 74
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 109
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 139
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 109
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 109
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 139
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 109
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 74
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 109
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 87
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 106
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 117
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 90
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 117
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 113
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 114
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 81
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 78
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 81
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 75
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 49
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 82
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 117
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 117
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 109
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 85
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 87
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 90
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 90
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 87
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 60
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 63
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 42
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 50
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 81
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 102
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 104
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 95
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 75
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 68
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 47
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 54
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 87
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 110
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 90
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 40
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 82
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 111
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 85
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 60
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 90
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 105
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 111
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 87
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 85
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 105
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 112
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 85
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 110
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 85
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 82
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 54
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 78
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 60
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 81
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 85
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 69
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 81
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 82
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 85
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 60
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 54
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 60
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 54
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 35
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 54
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 81
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 87
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 78
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 60
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 42
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 75
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 75
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 102
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 82
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 75
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 104
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 102
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 75
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 78
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 87
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 81
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 74
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 54
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 56
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 42
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 43
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 49
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 51
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 67
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 56
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 54
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 73
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 73
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 56
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 51
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 67
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 73
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 67
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 49
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 49
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 56
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 56
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 49
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 35
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 35
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 43
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 47
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 47
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 43
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 35
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 26
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 29
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 30
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 29
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 26
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 21
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 12
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
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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:
2,3 2,0,8,4 2,0,0,10,0,15,0,10,0,5 2,0,0,0,12,0,0,12,6,12,0,0,12,6,24,0,0,12,24,4,0,0,0,6
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 2\ q + 3\ q^{2}$
$F_{4} = 2\ q + 8\ q^{3} + 4\ q^{4}$
$F_{5} = 2\ q + 10\ q^{4} + 15\ q^{6} + 10\ q^{8} + 5\ q^{10}$
$F_{6} = 2\ q + 12\ q^{5} + 12\ q^{8} + 6\ q^{9} + 12\ q^{10} + 12\ q^{13} + 6\ q^{14} + 24\ q^{15} + 12\ q^{18} + 24\ q^{19} + 4\ q^{20} + 6\ q^{24}$
$F_{7} = 2\ q + 14\ q^{6} + 14\ q^{10} + 14\ q^{12} + 14\ q^{15} + 14\ q^{19} + 7\ q^{20} + 14\ q^{21} + 28\ q^{24} + 14\ q^{27} + 14\ q^{28} + 28\ q^{29} + 28\ q^{30} + 28\ q^{32} + 28\ q^{33} + 14\ q^{36} + 7\ q^{38} + 14\ q^{40} + 28\ q^{41} + 14\ q^{42} + 14\ q^{43} + 28\ q^{44} + 28\ q^{53} + 14\ q^{54} + 7\ q^{66}$
Description
The number of meanders with top half given by the noncrossing matching corresponding to the Dyck path.
Map
Delest-Viennot
Description
Return the Dyck path corresponding to the parallelogram polyomino obtained by applying Delest-Viennot's bijection.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
The Delest-Viennot bijection $\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path $(\gamma^{(-1)}\circ\beta)(D)$.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
The Delest-Viennot bijection $\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path $(\gamma^{(-1)}\circ\beta)(D)$.
Map
zeta map
Description
The zeta map on Dyck paths.
The zeta map $\zeta$ is a bijection on Dyck paths of semilength $n$.
It was defined in [1, Theorem 1], see also [2, Theorem 3.15] and sends the bistatistic (area, dinv) to the bistatistic (bounce, area). It is defined by sending a Dyck path $D$ with corresponding area sequence $a=(a_1,\ldots,a_n)$ to a Dyck path as follows:
The zeta map $\zeta$ is a bijection on Dyck paths of semilength $n$.
It was defined in [1, Theorem 1], see also [2, Theorem 3.15] and sends the bistatistic (area, dinv) to the bistatistic (bounce, area). It is defined by sending a Dyck path $D$ with corresponding area sequence $a=(a_1,\ldots,a_n)$ to a Dyck path as follows:
- First, build an intermediate Dyck path consisting of $d_1$ north steps, followed by $d_1$ east steps, followed by $d_2$ north steps and $d_2$ east steps, and so on, where $d_i$ is the number of $i-1$'s within the sequence $a$.
For example, given $a=(0,1,2,2,2,3,1,2)$, we build the path
$$NE\ NNEE\ NNNNEEEE\ NE.$$ - Next, the rectangles between two consecutive peaks are filled. Observe that such the rectangle between the $k$th and the $(k+1)$st peak must be filled by $d_k$ east steps and $d_{k+1}$ north steps. In the above example, the rectangle between the second and the third peak must be filled by $2$ east and $4$ north steps, the $2$ being the number of $1$'s in $a$, and $4$ being the number of $2$'s. To fill such a rectangle, scan through the sequence a from left to right, and add east or north steps whenever you see a $k-1$ or $k$, respectively. So to fill the $2\times 4$ rectangle, we look for $1$'s and $2$'s in the sequence and see $122212$, so this rectangle gets filled with $ENNNEN$.
The complete path we obtain in thus
$$NENNENNNENEEENEE.$$
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