Identifier
-
Mp00327:
Dyck paths
—inverse Kreweras complement⟶
Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St000012: Dyck paths ⟶ ℤ (values match St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2.)
Values
[1,0] => [1,0] => [1,0] => 0
[1,0,1,0] => [1,1,0,0] => [1,0,1,0] => 0
[1,1,0,0] => [1,0,1,0] => [1,1,0,0] => 1
[1,0,1,0,1,0] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 0
[1,0,1,1,0,0] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 2
[1,1,0,1,0,0] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[1,1,1,0,0,0] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => 4
[1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => 5
[1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0] => 5
[1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0] => 5
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0] => 6
[1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 5
[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] => 7
[1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 7
[1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0] => 8
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0] => 6
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 5
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 7
[1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => 9
[1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => 4
[1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 6
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0] => 8
[1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 7
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 8
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 7
>>> Load all 1200 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 9
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 6
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 8
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 10
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 7
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 6
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 8
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 8
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 9
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 7
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 10
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 7
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 9
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 11
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 7
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 8
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 6
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 9
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 6
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 9
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 10
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 11
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 10
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 12
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 5
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 5
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 6
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 5
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 5
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 7
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 8
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 9
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 7
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 6
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 8
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 10
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 7
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 11
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 12
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 13
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 5
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 6
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 6
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 8
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 8
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 9
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 11
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 7
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 10
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 12
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 14
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 9
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 11
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 13
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 15
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 7
[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] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 7
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 8
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 7
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 9
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 6
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 8
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 10
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 7
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 6
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 8
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 9
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 7
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 6
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 10
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 7
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 9
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 11
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4
[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] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 7
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 8
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 7
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 9
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 6
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 8
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 9
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 10
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 11
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 10
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 12
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 5
[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] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 6
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 5
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 7
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 9
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 8
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 10
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 7
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 9
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 11
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 12
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 13
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 6
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 8
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 8
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 9
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 11
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 7
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 10
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 12
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 14
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 9
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 11
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 13
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 15
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 8
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 7
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 9
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 9
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 10
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 8
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 7
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 9
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 11
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 8
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 10
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 12
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 10
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 11
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 12
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 11
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 13
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 9
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 10
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 8
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 7
[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] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 9
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 11
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 8
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 10
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 12
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 13
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 14
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 9
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 9
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 8
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 11
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 13
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 15
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 10
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 14
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 16
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 7
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 6
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 8
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 8
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 9
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 7
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 6
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 8
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 10
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 7
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 9
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 7
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[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] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[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] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 7
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 8
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 6
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[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] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 7
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 9
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 6
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 8
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 10
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 9
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 10
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 10
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 12
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 5
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 7
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 8
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 9
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3
[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] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 4
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 7
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 8
[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] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 10
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 7
[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] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 9
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 12
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 13
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 6
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 8
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 9
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 7
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 10
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 12
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 14
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 9
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11
[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] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 13
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 15
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 11
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 12
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 13
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 12
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 14
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 14
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 15
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 13
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 12
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 14
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 16
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 13
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 15
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 17
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 6
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 7
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 6
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 6
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 6
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 7
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 6
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 6
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 8
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 8
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 9
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 6
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 7
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 7
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 7
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 6
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 8
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 10
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 8
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 7
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 9
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 10
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 11
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 12
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 11
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 13
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 6
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 9
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 10
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 8
[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] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 7
[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] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 9
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 11
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 8
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 10
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 12
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 13
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 14
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 5
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 6
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 6
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 9
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 9
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 10
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 12
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 8
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 11
[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] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 13
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 15
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 10
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 12
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 14
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 16
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 15
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 16
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 17
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 16
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 18
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 6
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 7
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 8
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 8
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 8
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 9
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 9
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 10
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 11
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 10
[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] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 10
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 11
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 12
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 11
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 11
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 13
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 14
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 15
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 6
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 7
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 7
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 9
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 9
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 10
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 13
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 6
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 8
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 12
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 14
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 16
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 8
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 10
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 13
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 15
[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] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 17
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 18
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 19
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 10
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 9
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 11
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 12
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 12
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 14
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 9
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 14
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 15
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 17
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 9
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 11
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 16
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 18
[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] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 20
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 13
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 15
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 17
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 19
[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] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 21
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 7
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 8
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 7
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 9
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 6
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 8
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 10
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 7
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 8
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 8
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 9
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 7
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 6
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 10
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 7
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 9
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 11
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 7
[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] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 7
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 8
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 6
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 7
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 9
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 6
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 8
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 9
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 10
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 11
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 10
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 12
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 6
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 7
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 8
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 9
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 7
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 6
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 8
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 10
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 7
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 9
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 11
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 12
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 13
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 5
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 6
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 8
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 8
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 9
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 11
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 7
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 10
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 12
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 14
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 9
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 11
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 13
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 15
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 8
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 7
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 9
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 9
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 10
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 8
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 7
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 9
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 11
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 8
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 10
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 12
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 10
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 11
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 12
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 11
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 13
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 9
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 10
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 8
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 7
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 9
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 11
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 8
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 10
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 12
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 13
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 14
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 9
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 9
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 8
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 11
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 13
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 15
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 10
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 12
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 14
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 16
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 7
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 8
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 8
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 9
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 7
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 8
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 10
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 7
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 9
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 6
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 7
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[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] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 7
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 8
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 7
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 9
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 6
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 8
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 10
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 9
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 10
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 10
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 12
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 7
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 8
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 9
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 7
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 8
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 10
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 7
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 9
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 12
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 13
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 8
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 9
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 7
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 10
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 12
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 14
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 9
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 13
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 15
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 11
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 12
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 13
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 12
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 14
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 14
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 15
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 13
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 12
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 14
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 16
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 13
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 15
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 17
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 6
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 7
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 6
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 7
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 8
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 8
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 9
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 6
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 7
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 7
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 7
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 6
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 8
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 10
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 8
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 7
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 9
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 10
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 11
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 12
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 11
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 13
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 5
[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] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 6
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 9
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 10
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 9
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 11
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 8
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 10
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 12
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 13
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 14
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 9
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 9
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 10
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 12
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 8
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 11
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 13
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 15
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 10
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 12
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 14
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 16
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 15
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 16
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 17
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 16
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 18
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 6
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 7
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 8
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 8
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 8
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 9
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 7
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 9
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 10
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 11
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 5
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 10
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 10
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 11
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 12
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 11
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 11
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 13
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 14
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 15
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 7
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 7
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 9
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 9
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 10
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 13
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 6
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 8
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 14
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 16
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 8
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 10
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 13
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 15
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 17
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 18
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 19
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 10
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 9
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 11
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 12
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 12
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 14
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 9
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 14
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 15
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 17
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 9
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 11
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 16
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 18
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 20
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 13
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 15
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 17
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 19
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 21
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[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] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 7
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 8
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[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] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 7
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 7
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 8
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 9
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 7
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 6
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 8
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 10
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 9
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 11
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 8
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 7
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 9
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 9
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 10
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 8
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 7
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 9
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 11
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 8
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 10
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 12
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 7
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 6
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 8
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 5
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 3
[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] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 6
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 7
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 9
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 5
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 7
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 6
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 10
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 7
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 9
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 11
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 10
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 11
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 12
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 11
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 13
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 6
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 6
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 7
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 6
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 6
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 9
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 10
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 4
[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] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 8
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 7
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 9
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 11
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 8
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 10
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 12
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 13
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 14
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 6
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 7
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 9
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 9
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 10
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 6
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 8
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 11
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 13
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 15
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 10
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 12
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 14
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 16
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,2,1,1 1,3,3,3,2,1,1 1,4,6,7,7,5,5,3,2,1,1 1,5,10,14,17,16,16,14,11,9,7,5,3,2,1,1 1,6,15,25,35,40,43,44,40,37,32,28,22,18,13,11,7,5,3,2,1,1
F1=1
F2=1+q
F3=1+2 q+q2+q3
F4=1+3 q+3 q2+3 q3+2 q4+q5+q6
F5=1+4 q+6 q2+7 q3+7 q4+5 q5+5 q6+3 q7+2 q8+q9+q10
F6=1+5 q+10 q2+14 q3+17 q4+16 q5+16 q6+14 q7+11 q8+9 q9+7 q10+5 q11+3 q12+2 q13+q14+q15
F7=1+6 q+15 q2+25 q3+35 q4+40 q5+43 q6+44 q7+40 q8+37 q9+32 q10+28 q11+22 q12+18 q13+13 q14+11 q15+7 q16+5 q17+3 q18+2 q19+q20+q21
Description
The area of a Dyck path.
This is the number of complete squares in the integer lattice which are below the path and above the x-axis. The 'half-squares' directly above the axis do not contribute to this statistic.
1. Dyck paths are bijection with area sequences (a1,…,an) such that a1=0,ak+1≤ak+1.
2. The generating function Dn(q)=∑D∈Dnqarea(D) satisfy the recurrence Dn+1(q)=∑qkDk(q)Dn−k(q).
3. The area is equidistributed with St000005The bounce statistic of a Dyck path. and St000006The dinv of a Dyck path.. Pairs of these statistics play an important role in the theory of q,t-Catalan numbers.
This is the number of complete squares in the integer lattice which are below the path and above the x-axis. The 'half-squares' directly above the axis do not contribute to this statistic.
1. Dyck paths are bijection with area sequences (a1,…,an) such that a1=0,ak+1≤ak+1.
2. The generating function Dn(q)=∑D∈Dnqarea(D) satisfy the recurrence Dn+1(q)=∑qkDk(q)Dn−k(q).
3. The area is equidistributed with St000005The bounce statistic of a Dyck path. and St000006The dinv of a Dyck path.. Pairs of these statistics play an important role in the theory of q,t-Catalan numbers.
Map
decomposition reverse
Description
This map is recursively defined as follows.
The unique empty path of semilength 0 is sent to itself.
Let D be a Dyck path of semilength n>0 and decompose it into 1D10D2 with Dyck paths D1,D2 of respective semilengths n1 and n2 such that n1 is minimal. One then has n1+n2=n−1.
Now let ˜D1 and ˜D2 be the recursively defined respective images of D1 and D2 under this map. The image of D is then defined as 1˜D20˜D1.
The unique empty path of semilength 0 is sent to itself.
Let D be a Dyck path of semilength n>0 and decompose it into 1D10D2 with Dyck paths D1,D2 of respective semilengths n1 and n2 such that n1 is minimal. One then has n1+n2=n−1.
Now let ˜D1 and ˜D2 be the recursively defined respective images of D1 and D2 under this map. The image of D is then defined as 1˜D20˜D1.
Map
inverse Kreweras complement
Description
Return the inverse of the Kreweras complement of a Dyck path, regarded as a noncrossing set partition.
To identify Dyck paths and noncrossing set partitions, this maps uses the following classical bijection. The number of down steps after the i-th up step of the Dyck path is the size of the block of the set partition whose maximal element is i. If i is not a maximal element of a block, the (i+1)-st step is also an up step.
To identify Dyck paths and noncrossing set partitions, this maps uses the following classical bijection. The number of down steps after the i-th up step of the Dyck path is the size of the block of the set partition whose maximal element is i. If i is not a maximal element of a block, the (i+1)-st step is also an up step.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!