Identifier
-
Mp00120:
Dyck paths
—Lalanne-Kreweras involution⟶
Dyck paths
Mp00100: Dyck paths —touch composition⟶ Integer compositions
St000047: Integer compositions ⟶ ℤ
Values
[1,0] => [1,0] => [1] => 1
[1,0,1,0] => [1,1,0,0] => [2] => 1
[1,1,0,0] => [1,0,1,0] => [1,1] => 1
[1,0,1,0,1,0] => [1,1,1,0,0,0] => [3] => 1
[1,0,1,1,0,0] => [1,1,0,0,1,0] => [2,1] => 2
[1,1,0,0,1,0] => [1,0,1,1,0,0] => [1,2] => 1
[1,1,0,1,0,0] => [1,1,0,1,0,0] => [3] => 1
[1,1,1,0,0,0] => [1,0,1,0,1,0] => [1,1,1] => 1
[1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [4] => 1
[1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => [3,1] => 3
[1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [2,2] => 3
[1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => [4] => 1
[1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => [2,1,1] => 3
[1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => [1,3] => 1
[1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => [1,2,1] => 2
[1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => [4] => 1
[1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => [4] => 1
[1,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0] => [3,1] => 3
[1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => [1,1,2] => 1
[1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0] => [1,3] => 1
[1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0] => [4] => 1
[1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => [1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => [5] => 1
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => [4,1] => 4
[1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => [3,2] => 6
[1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => [5] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => [3,1,1] => 6
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => [2,3] => 4
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => [2,2,1] => 8
[1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => [5] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => [5] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => [4,1] => 4
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => [2,1,2] => 4
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => [2,3] => 4
[1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => [5] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => [1,4] => 1
[1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => [1,3,1] => 3
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => [1,2,2] => 3
[1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => [1,4] => 1
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => 3
[1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => [5] => 1
[1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [4,1] => 4
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => [5] => 1
[1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => [5] => 1
[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => [4,1] => 4
[1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => [3,2] => 6
[1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => [5] => 1
[1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => [5] => 1
[1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => [3,1,1] => 6
[1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => [1,1,3] => 1
[1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => 2
[1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => [1,4] => 1
[1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => [1,4] => 1
[1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => [1,3,1] => 3
[1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => [5] => 1
[1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [5] => 1
[1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => [5] => 1
[1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => [4,1] => 4
[1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => 1
[1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => [1,1,3] => 1
[1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => [1,4] => 1
[1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => [5] => 1
[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] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => 5
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => 10
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => 10
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => 10
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => 20
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [6] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [6] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [5,1] => 5
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => 10
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,3] => 10
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [6] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => 10
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => 5
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => 15
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => 15
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,4] => 5
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => 15
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [6] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [5,1] => 5
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [6] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [6] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,1] => 5
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [4,2] => 10
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [6] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [6] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,1] => 10
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => 5
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => 10
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,4] => 5
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,4] => 5
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1] => 15
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [6] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [6] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [6] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [5,1] => 5
>>> Load all 2815 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => 5
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3] => 5
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,4] => 5
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [6] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => 6
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => 6
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => 8
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,5] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,5] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,1] => 4
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => 4
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3] => 4
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,5] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [6] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [5,1] => 5
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => [4,2] => 10
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [6] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => [4,1,1] => 10
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [6] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,1] => 5
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [6] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [6] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 5
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,2] => 10
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [6] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [6] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,1] => 10
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,3] => 10
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => [3,2,1] => 20
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [6] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [6] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [5,1] => 5
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [6] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [6] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [6] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => [5,1] => 5
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,2] => 10
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => [3,3] => 10
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [6] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [6] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1] => 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] => [1,1,4] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,4] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,5] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,4,1] => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,5] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,1] => 4
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2] => 6
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,5] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,1,1] => 6
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [6] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => [5,1] => 5
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [6] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [6] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => [5,1] => 5
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [6] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [6] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [6] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,1] => 5
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => [4,2] => 10
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [6] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [6] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [6] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => [4,1,1] => 10
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,4] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,4] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,3,1] => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,5] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,5] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,5] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,4,1] => 4
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [6] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [6] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [6] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [6] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => [5,1] => 5
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,3] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,4] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,5] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [6] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1] => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,2] => 15
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,1] => 15
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3] => 20
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => 40
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [7] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,1] => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => 20
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3] => 20
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => 20
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4] => 15
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => 45
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => 45
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4] => 15
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => 45
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,1] => 6
[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] => [7] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1] => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2] => 15
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,1] => 15
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => 15
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => 30
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4] => 15
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4] => 15
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => 45
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [7] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [7] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,1] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => 15
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => 15
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4] => 15
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => 15
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5] => 6
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => 24
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => 36
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,5] => 6
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,1] => 36
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => 24
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,1] => 48
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,5] => 6
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,5] => 6
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1] => 24
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => 24
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,3] => 24
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,5] => 6
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => 24
[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] => [7] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,1] => 6
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,2] => 15
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => 15
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,1] => 6
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1] => 6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,2] => 15
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,1] => 15
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,3] => 20
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => 40
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [7] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,1] => 6
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [7] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,1] => 6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => 20
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [4,3] => 20
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => 20
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => 6
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => 18
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => 18
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,4] => 6
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => 18
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,5] => 6
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1] => 24
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,5] => 6
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,5] => 6
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,4,1] => 24
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,2] => 36
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,5] => 6
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,5] => 6
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,1] => 36
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [7] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,1] => 6
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [7] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [7] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,1] => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,1] => 6
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,2] => 15
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => 15
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => 6
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => 12
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,4] => 6
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4] => 6
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,1] => 18
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,5] => 6
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,5] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,5] => 6
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,4,1] => 24
[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] => [7] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [7] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [7] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,1] => 6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => 6
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,3] => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4] => 6
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,5] => 6
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => 6
[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] => [1,6] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,5,1] => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2] => 10
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,4,1,1] => 10
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => 10
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => 20
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,6] => 1
[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] => [1,6] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,1] => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,1,2] => 10
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,3] => 10
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,6] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => 10
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4] => 5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,3,1] => 15
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2] => 15
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4] => 5
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,1,1] => 15
[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] => [1,6] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,5,1] => 5
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,6] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,1] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2] => 10
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,6] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,1,1] => 10
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,2,1] => 10
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4] => 5
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,3,1] => 15
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,6] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,6] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,6] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,5,1] => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,2] => 5
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,3] => 5
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4] => 5
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,6] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [7] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1] => 6
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,2] => 15
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => 15
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,3] => 20
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => 40
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [7] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [7] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,1] => 6
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => 20
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3] => 20
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => 20
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1] => 6
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2] => 15
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [7] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => 15
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1] => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,2] => 15
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [7] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,1] => 15
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,3] => 20
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => 40
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [7] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,1] => 6
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [7] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,1] => 6
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => 20
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,3] => 20
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [7] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => 20
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4] => 15
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => 45
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => 45
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,4] => 15
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => 45
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [7] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,1] => 6
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [7] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,1] => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,2] => 15
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => 15
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [7] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,1] => 6
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,1] => 6
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,1] => 6
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2] => 15
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [7] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => 15
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => 15
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => 30
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,4] => 15
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,4] => 15
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => 45
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [7] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [7] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,1] => 6
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [7] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [7] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,1] => 6
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => 15
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => 15
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,4] => 15
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => 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] => [1,1,5] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,4,1] => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => 6
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,5] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,3,1,1] => 6
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,3] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,1] => 8
[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] => [1,1,5] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,5] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,4,1] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,2,1,2] => 4
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,2,3] => 4
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,5] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1] => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,6] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,5,1] => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,4,2] => 10
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,6] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,4,1,1] => 10
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,6] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,5,1] => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,6] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6] => 1
[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] => [1,5,1] => 5
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,2] => 10
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,1,1] => 10
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,3] => 10
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,2,1] => 20
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,6] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,6] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,5,1] => 5
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,6] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,6] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,6] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,1] => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,1,2] => 10
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,3] => 10
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,6] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,6] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => 10
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [7] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,1] => 6
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,2] => 15
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => 15
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [7] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,1] => 6
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [7] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,1] => 6
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,2] => 15
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [7] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => 15
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,1] => 6
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,1] => 6
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,1] => 6
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2] => 15
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => 15
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,3] => 20
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => 40
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [7] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,1] => 6
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [7] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [7] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,1] => 6
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [7] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,1] => 6
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => 20
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [4,3] => 20
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => 20
[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] => [1,1,1,4] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,3,1] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2] => 3
[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] => [1,1,1,4] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,2,1,1] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,5] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,4,1] => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,5] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,5] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,4,1] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,3,2] => 6
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,5] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,5] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,3,1,1] => 6
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,6] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,5,1] => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,6] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,6] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,5,1] => 5
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,6] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,6] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,6] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,5,1] => 5
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,4,2] => 10
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,6] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,6] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,4,1,1] => 10
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,1] => 6
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [7] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [7] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,1] => 6
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [7] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [7] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,1] => 6
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,1] => 6
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,2] => 15
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => 15
[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] => [1,1,1,1,3] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,2,1] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,4] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,4] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,3,1] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,5] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,5] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,5] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,4,1] => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,6] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,6] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,6] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,6] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,5,1] => 5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [7] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [7] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [6,1] => 6
[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] => [1,1,1,1,1,2] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,3] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,4] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,5] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,6] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7] => 1
[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] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,2] => 21
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,3] => 35
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => 70
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [8] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,1] => 7
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,3] => 35
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [8] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 35
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => 35
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => 105
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => 105
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => 35
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => 105
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [8] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,1] => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8] => 1
[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] => [8] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,1] => 7
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,2] => 21
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [8] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [8] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => 21
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 70
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => 35
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => 35
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => 105
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [8] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [8] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8] => 1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [7,1] => 7
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => 35
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [8] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => 35
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5] => 21
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => 84
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => 126
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,5] => 21
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => 126
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => 84
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => 168
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,5] => 21
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,5] => 21
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,4,1] => 84
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => 84
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,3] => 84
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,5] => 21
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => 84
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [8] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => 7
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [6,2] => 21
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [8] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => 21
[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] => [8] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,1] => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,1] => 7
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,2] => 21
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [8] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [8] => 1
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [5,3] => 35
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => 70
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [8] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [8] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => 7
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [8] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [8] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8] => 1
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,1] => 7
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [5,3] => 35
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [8] => 1
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [8] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => 35
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 63
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 63
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => 63
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,5] => 21
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,4,1] => 84
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,5] => 21
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,5] => 21
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,4,1] => 84
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,3,2] => 126
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,5] => 21
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5] => 21
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,3,1,1] => 126
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [8] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => 7
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [8] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [8] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => 7
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [8] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8] => 1
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,1] => 7
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [6,2] => 21
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [8] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [8] => 1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [8] => 1
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => 21
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 21
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,3,1] => 63
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,5] => 21
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,5] => 21
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,5] => 21
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,4,1] => 84
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [8] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [8] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [8] => 1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8] => 1
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => 7
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => 21
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,5] => 21
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [8] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 21
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,6] => 7
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,5,1] => 35
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,2] => 70
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,6] => 7
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,3] => 70
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => 140
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,6] => 7
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,6] => 7
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1] => 35
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => 70
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,3] => 70
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,6] => 7
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => 70
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => 35
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => 105
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => 105
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,4] => 35
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => 105
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,6] => 7
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,1] => 35
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,6] => 7
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,6] => 7
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1] => 35
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,4,2] => 70
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,6] => 7
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,6] => 7
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => 35
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => 70
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,4] => 35
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,2,4] => 35
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,3,1] => 105
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,6] => 7
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,6] => 7
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,6] => 7
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,5,1] => 35
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => 35
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,2,1,3] => 35
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,4] => 35
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,6] => 7
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 35
[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] => [8] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,1] => 7
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [6,2] => 21
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [8] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [5,3] => 35
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => 70
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [8] => 1
[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] => [8] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [7,1] => 7
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [5,3] => 35
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [8] => 1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 35
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => 7
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,2] => 21
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [8] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,1] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,1] => 7
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,2] => 21
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [8] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [8] => 1
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3] => 35
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => 70
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [8] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [8] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => 7
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [8] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [8] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8] => 1
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [7,1] => 7
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [5,3] => 35
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [8] => 1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [8] => 1
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 35
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4] => 35
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => 105
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => 105
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,4] => 35
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => 105
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [8] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [7,1] => 7
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [8] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [8] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,1] => 7
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [6,2] => 21
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [8] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [8] => 1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => 21
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [8] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => 7
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => 7
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [8] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [8] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8] => 1
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,1] => 7
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [6,2] => 21
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [8] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [8] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [8] => 1
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => 21
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 70
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4] => 35
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [4,4] => 35
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => 105
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [8] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [8] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [8] => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [7,1] => 7
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [8] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [8] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [8] => 1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [8] => 1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => 7
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [4,4] => 35
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [8] => 1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [8] => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => 35
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => 28
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => 42
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => 42
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => 28
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => 56
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,1] => 28
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => 28
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,3] => 28
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => 28
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,6] => 7
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1] => 35
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,2] => 70
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,6] => 7
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,6] => 7
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1] => 35
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6] => 7
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,6] => 7
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,5,1] => 35
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,4,2] => 70
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,6] => 7
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6] => 7
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,3] => 70
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,2,1] => 140
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,6] => 7
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,6] => 7
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,5,1] => 35
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,6] => 7
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,6] => 7
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6] => 7
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1] => 35
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,2] => 70
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,3] => 70
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,6] => 7
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,6] => 7
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => 70
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [8] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [7,1] => 7
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [6,2] => 21
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [8] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [8] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,1] => 7
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [8] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [8] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [7,1] => 7
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [6,2] => 21
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [8] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [8] => 1
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [8] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => 7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => 7
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8] => 1
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,1] => 7
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,2] => 21
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [8] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [8] => 1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [8] => 1
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [5,3] => 35
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => 70
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [8] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [8] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [7,1] => 7
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [8] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [8] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [8] => 1
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [7,1] => 7
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [8] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [8] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [8] => 1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8] => 1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => 7
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [5,3] => 35
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [8] => 1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [8] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [8] => 1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => 35
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => 21
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => 21
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => 21
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,1] => 28
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,1] => 28
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,2] => 42
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,3,1,1] => 42
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,6] => 7
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,5,1] => 35
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,6] => 7
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,6] => 7
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,1] => 35
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,6] => 7
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,6] => 7
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6] => 7
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,1] => 35
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,2] => 70
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,6] => 7
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,6] => 7
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,6] => 7
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [8] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [7,1] => 7
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [8] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [8] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [7,1] => 7
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [8] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [8] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [8] => 1
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [7,1] => 7
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [8] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8] => 1
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => 7
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [6,2] => 21
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [8] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [8] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [8] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [8] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => 21
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 14
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,3,1] => 21
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,1] => 28
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,6] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,6] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,6] => 7
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,6] => 7
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,5,1] => 35
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [8] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [8] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [8] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [8] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [7,1] => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => 7
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,6] => 7
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,7] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,6,1] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,5,2] => 15
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,5,1,1] => 15
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,4,3] => 20
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => 40
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,7] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,1] => 6
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => 20
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,4,3] => 20
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,7] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => 20
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => 15
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => 45
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => 45
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,3,4] => 15
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => 45
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,7] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,6,1] => 6
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,7] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,6,1] => 6
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,5,2] => 15
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,7] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7] => 1
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => 15
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => 15
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => 30
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,3,4] => 15
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,3,4] => 15
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,3,3,1] => 45
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,7] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,7] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,7] => 1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,6,1] => 6
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => 15
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => 15
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,3,4] => 15
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,7] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => 15
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,5] => 6
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,1] => 24
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,2] => 36
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,5] => 6
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,1,1] => 36
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,3] => 24
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => 48
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5] => 6
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,5] => 6
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,1] => 24
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => 24
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,3] => 24
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5] => 6
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => 24
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,7] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,6,1] => 6
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,5,2] => 15
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,7] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,5,1,1] => 15
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,7] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,6,1] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,7] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,1] => 6
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2] => 15
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,7] => 1
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => 15
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3] => 20
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,1] => 40
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,7] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,7] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,6,1] => 6
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,7] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,7] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,7] => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,6,1] => 6
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => 20
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3] => 20
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,7] => 1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,7] => 1
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => 20
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => 6
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => 18
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => 18
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,1,4] => 6
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => 18
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,5] => 6
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,1] => 24
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5] => 6
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,5] => 6
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,4,1] => 24
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,2] => 36
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,5] => 6
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5] => 6
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,1,1] => 36
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,7] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,6,1] => 6
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,7] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,7] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,6,1] => 6
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,7] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,7] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,7] => 1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,6,1] => 6
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,5,2] => 15
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,7] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,7] => 1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,7] => 1
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,5,1,1] => 15
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => 6
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => 12
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,4] => 6
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,4] => 6
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,3,1] => 18
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,5] => 6
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,5] => 6
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5] => 6
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,1] => 24
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,7] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,7] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,7] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,7] => 1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,6,1] => 6
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => 6
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,3] => 6
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,4] => 6
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,5] => 6
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,7] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [8] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2] => 21
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [8] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,3] => 35
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => 70
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [8] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [8] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => 7
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,3] => 35
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [8] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 35
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => 35
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => 105
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => 105
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => 35
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => 105
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [8] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [8] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [8] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,2] => 21
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [8] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [8] => 1
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 70
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => 35
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => 35
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => 105
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [8] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [8] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [8] => 1
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => 7
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => 35
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [8] => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => 35
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2] => 21
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [8] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,3] => 35
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => 70
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [8] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => 7
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [5,3] => 35
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [8] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 35
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,2] => 21
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [8] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,2] => 21
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [8] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [8] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3] => 35
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => 70
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [8] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [8] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8] => 1
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [7,1] => 7
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3] => 35
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [8] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [8] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 35
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => 35
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => 105
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => 105
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => 35
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => 105
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [8] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [6,2] => 21
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [8] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [8] => 1
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [8] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [8] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [8] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [8] => 1
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [6,2] => 21
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [8] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [8] => 1
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [8] => 1
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 70
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => 35
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => 35
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => 105
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [8] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [8] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8] => 1
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => 7
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [8] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [8] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8] => 1
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => 7
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => 35
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [8] => 1
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [8] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => 35
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5] => 21
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => 84
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => 126
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,5] => 21
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => 126
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => 84
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => 168
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,5] => 21
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,5] => 21
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,4,1] => 84
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => 84
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,3] => 84
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,5] => 21
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => 84
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [8] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,2] => 21
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [8] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [8] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [8] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [8] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2] => 21
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [8] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [8] => 1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,3] => 35
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => 70
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [8] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [8] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [8] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [8] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,3] => 35
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [8] => 1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [8] => 1
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => 35
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [8] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [6,2] => 21
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [8] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [8] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [8] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2] => 21
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [8] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [8] => 1
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [8] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,2] => 21
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [8] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [8] => 1
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [8] => 1
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [5,3] => 35
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => 70
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [8] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [8] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [8] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [8] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [8] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [8] => 1
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [8] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [5,3] => 35
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [8] => 1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [8] => 1
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [8] => 1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => 35
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 63
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 63
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => 63
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,5] => 21
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,4,1] => 84
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,5] => 21
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,5] => 21
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,4,1] => 84
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,3,2] => 126
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,5] => 21
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5] => 21
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,3,1,1] => 126
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [8] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [8] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [8] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [8] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [8] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [8] => 1
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,2] => 21
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [8] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [8] => 1
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [8] => 1
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [8] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [8] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [8] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [8] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [8] => 1
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [8] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [8] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8] => 1
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [6,2] => 21
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [8] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [8] => 1
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [8] => 1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [8] => 1
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 21
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,3,1] => 63
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,5] => 21
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,5] => 21
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,5] => 21
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,4,1] => 84
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [8] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [8] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [8] => 1
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [8] => 1
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [8] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [8] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [8] => 1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [8] => 1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => 21
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,5] => 21
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 21
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,6] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,5,1] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,4,2] => 10
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,6] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,4,1,1] => 10
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,3,3] => 10
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => 20
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,6] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,6] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,5,1] => 5
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => 10
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,3,3] => 10
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,6] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => 10
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,2,4] => 5
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,2,3,1] => 15
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2] => 15
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,4] => 5
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,2,2,1,1] => 15
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,6] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,5,1] => 5
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,6] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,6] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,5,1] => 5
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,4,2] => 10
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,6] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,6] => 1
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,4,1,1] => 10
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,2,1,3] => 5
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => 10
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,2,4] => 5
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,2,4] => 5
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,2,3,1] => 15
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,6] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,6] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,6] => 1
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,5,1] => 5
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => 5
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,2,1,3] => 5
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,4] => 5
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,6] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1] => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,6,1] => 6
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2] => 15
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,7] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => 15
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3] => 20
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => 40
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,6,1] => 6
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => 20
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3] => 20
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,7] => 1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => 20
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,6,1] => 6
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2] => 15
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => 15
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,6,1] => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7] => 1
[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] => [1,6,1] => 6
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,2] => 15
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,7] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,7] => 1
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => 15
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,3] => 20
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => 40
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,6,1] => 6
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,6,1] => 6
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => 20
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,3] => 20
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,7] => 1
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,7] => 1
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => 20
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => 15
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => 45
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => 45
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4] => 15
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => 45
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,6,1] => 6
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,6,1] => 6
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,5,2] => 15
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => 15
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,6,1] => 6
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,6,1] => 6
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,6,1] => 6
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2] => 15
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => 15
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => 15
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => 30
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4] => 15
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4] => 15
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,3,1] => 45
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,6,1] => 6
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,6,1] => 6
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => 15
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => 15
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4] => 15
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,7] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => 15
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [8] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,2] => 21
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [8] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,3] => 35
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => 70
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [8] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [8] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,3] => 35
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [8] => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 35
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [8] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2] => 21
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [8] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [8] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [8] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2] => 21
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [8] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [8] => 1
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,3] => 35
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => 70
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [8] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [8] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [8] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [8] => 1
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,3] => 35
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8] => 1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [8] => 1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 35
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2] => 21
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [8] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2] => 21
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [8] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [8] => 1
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,2] => 21
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [8] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [8] => 1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [8] => 1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,3] => 35
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => 70
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [8] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [8] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [8] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [8] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8] => 1
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [8] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [8] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8] => 1
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8] => 1
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,3] => 35
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [8] => 1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [8] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [8] => 1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 35
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4] => 35
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => 105
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => 105
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [4,4] => 35
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => 105
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [8] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [8] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [8] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,2] => 21
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [8] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [8] => 1
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [8] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [8] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [8] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [8] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [8] => 1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,2] => 21
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [8] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [8] => 1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [8] => 1
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [8] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [8] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [8] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [8] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8] => 1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [8] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [8] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [8] => 1
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [6,2] => 21
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [8] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [8] => 1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [8] => 1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [8] => 1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 70
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4] => 35
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,4] => 35
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => 105
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [8] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [8] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [8] => 1
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [8] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [8] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [8] => 1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [8] => 1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [8] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [8] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [8] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => 7
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [4,4] => 35
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8] => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [8] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => 35
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,5] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,4,1] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,3,2] => 6
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,5] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,3,1,1] => 6
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,2,3] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,1] => 8
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,5] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,5] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,4,1] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,2,1,2] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,2,3] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,5] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,6] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,5,1] => 5
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,4,2] => 10
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,6] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,4,1,1] => 10
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,6] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,5,1] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,6] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,6] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,5,1] => 5
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,4,2] => 10
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,6] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,6] => 1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,4,1,1] => 10
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,3,3] => 10
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => 20
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,6] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,6] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,5,1] => 5
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,6] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,6] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,6] => 1
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,5,1] => 5
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => 10
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,3,3] => 10
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,6] => 1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,6] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => 10
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,6,1] => 6
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,5,2] => 15
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,5,1,1] => 15
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,6,1] => 6
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,6,1] => 6
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,5,2] => 15
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => 15
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,6,1] => 6
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,6,1] => 6
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,6,1] => 6
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,5,2] => 15
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => 15
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,3] => 20
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,4,2,1] => 40
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,6,1] => 6
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,6,1] => 6
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,6,1] => 6
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => 20
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,4,3] => 20
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,7] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => 20
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,2] => 21
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [8] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,2] => 21
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [8] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [8] => 1
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2] => 21
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [8] => 1
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2] => 21
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [8] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [8] => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [8] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [8] => 1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,3] => 35
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => 70
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [8] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [8] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,1] => 7
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [8] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [8] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8] => 1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,1] => 7
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [8] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [8] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [8] => 1
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [8] => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => 7
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [8] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [8] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [8] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [8] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => 7
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,3] => 35
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [8] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => 35
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,4] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,3,1] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,4] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,2,1,1] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,5] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,4,1] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,5] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,5] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,4,1] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,3,2] => 6
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,5] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,5] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,3,1,1] => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,6] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,5,1] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,6] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,6] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,5,1] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,6] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,6] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,6] => 1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,5,1] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,4,2] => 10
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,6] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,6] => 1
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,6] => 1
[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] => [1,1,4,1,1] => 10
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,7] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,6,1] => 6
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,7] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,7] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,6,1] => 6
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,7] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,7] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,7] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,6,1] => 6
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,7] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,7] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,7] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,7] => 1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,6,1] => 6
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,5,2] => 15
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,7] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,7] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,7] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7] => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,5,1,1] => 15
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [8] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,1] => 7
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [8] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [8] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,1] => 7
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [8] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [8] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [8] => 1
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,1] => 7
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [8] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [8] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [8] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [8] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => 7
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [8] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => 7
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,2] => 21
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [8] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [8] => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [8] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => 21
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,3] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,2,1] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,4] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,4] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,3,1] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,5] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,5] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,5] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,4,1] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,6] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,6] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,6] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,6] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,5,1] => 5
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,7] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,7] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,7] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,7] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,7] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,6,1] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [8] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,1] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,2] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,3] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,4] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,5] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,6] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,7] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,2] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,2] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [9] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,8] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,2] => 28
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,7] => 8
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => 8
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,7] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => 1
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => 1
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 28
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,8] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,6] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,6,2] => 21
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [9] => 1
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9] => 1
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => 56
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,7] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,5] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,8] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,2] => 28
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,7] => 8
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => 8
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 70
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,6] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,4] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,8] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [9] => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,5,1,2] => 35
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,2] => 28
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,2,1] => 2
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,5,1] => 40
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => 1
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,1] => 8
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1] => 7
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 56
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,5] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,3] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [9] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,7] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,8] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,1] => 8
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => 8
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,8] => 1
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 28
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,1,4] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,8] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,2,1] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [9] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [9] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [9] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,7,1] => 7
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => 112
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,6] => 7
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => 7
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,3] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,8] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,3] => 56
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,6] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,8] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,4,1,2] => 20
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,2] => 28
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,1] => 8
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0] => [9] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,7] => 8
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0] => [8,1] => 8
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,8] => 1
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0] => [9] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,6] => 28
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => 28
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [8,1] => 8
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [6,3] => 56
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 56
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [7,1,1] => 28
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [7,1,1] => 28
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0] => [5,4] => 70
[1,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 70
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,1] => 8
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [4,5] => 56
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [9] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 56
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [9] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,1] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [9] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [9] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => 28
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [9] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [9] => 1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [9] => 1
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 70
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [9] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [8,1] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [9] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [9] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,1] => 8
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [9] => 1
[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [9] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [9] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [9] => 1
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 70
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,6] => 28
[1,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [3,3,1,1,1] => 280
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [9] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [9] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [9] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,6] => 28
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [9] => 1
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [9] => 1
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0] => [9] => 1
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 28
[1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,1] => 112
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [9] => 1
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => 1
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => 8
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [9] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => 1
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => 1
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => 8
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,6] => 28
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 28
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,7,1] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,8] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,6,1,1] => 21
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,8] => 1
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,8] => 1
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => 35
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,8] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,7,1] => 7
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,8] => 1
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,8] => 1
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => 7
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,8] => 1
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,8] => 1
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1] => 21
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [9] => 1
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 56
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 70
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [9] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [8,1] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [9] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [9] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,1] => 8
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [9] => 1
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [9] => 1
[1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0] => [9] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4] => 70
[1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [9] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [9] => 1
[1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 70
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [9] => 1
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [9] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [9] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [9] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [9] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,5] => 56
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [4,4,1] => 224
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 28
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [9] => 1
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,1] => 8
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,5] => 56
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [4,4,1] => 224
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [9] => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [9] => 1
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [9] => 1
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,1] => 8
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [4,5] => 56
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 56
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,7] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,6,1] => 6
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,7] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,7] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,7] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,7] => 1
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1] => 15
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,8] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,8] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,8] => 1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,8] => 1
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,8] => 1
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,8] => 1
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => 35
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [9] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [9] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [9] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [8,1] => 8
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0] => [9] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [9] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [9] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [9] => 1
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [9] => 1
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 56
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [9] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [9] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [9] => 1
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [9] => 1
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => 28
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [5,3,1] => 210
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [9] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [9] => 1
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,1] => 8
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4] => 70
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 70
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,6] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,6] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,6] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,6] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,3,1,1,1] => 10
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,7] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,7] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,7] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,8] => 1
[1,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,8] => 1
[1,1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,1,1] => 21
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,5,3] => 35
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => 28
[1,1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => 28
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [9] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [9] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [9] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [9] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [9] => 1
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,1] => 8
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [9] => 1
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [9] => 1
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => 28
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,1] => 8
[1,1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,1] => 8
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [9] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,3] => 56
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [9] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [9] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [9] => 1
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [9] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => 56
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,5] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,4,1] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,5] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,5] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,3,1,1] => 6
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,6] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,6,1] => 6
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,8] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,8] => 1
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,1] => 7
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,8] => 1
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,8] => 1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,6,1,1] => 21
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,1] => 8
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => 1
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => 8
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [9] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [9] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => 8
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [9] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [9] => 1
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 28
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,4] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,3,1] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,5] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,5] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,4,1] => 4
[1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,6] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,7] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,7] => 1
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,6,1] => 6
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,8] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,8] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8] => 1
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [9] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,3] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,4] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,5] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,6] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,7] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,8] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [9] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [9] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [9] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [9] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [9] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => 28
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,3] => 56
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4] => 70
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,5] => 56
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,6] => 28
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [9] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [9] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 56
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [9] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [9] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [9] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [9] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [9] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [9] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [9] => 1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0] => [9] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,8] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [8,1] => 8
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 70
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0] => [9] => 1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [9] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [9] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [9] => 1
[1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 28
[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [4,5] => 56
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4] => 70
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => [9] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [3,6] => 28
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,7] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [9] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [8,1] => 8
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => 1
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 56
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [9] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [3,6] => 28
[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [9] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [9] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,6] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,2] => 28
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => 56
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => 112
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => 70
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => 210
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,2,1,1] => 210
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => 56
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => 224
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,3,2] => 336
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => 448
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,2,1,1,1] => 224
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,6] => 28
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,4,2] => 280
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2,2] => 420
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,1,1,1] => 140
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,1] => 112
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,7] => 8
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,4,3] => 160
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4] => 120
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,5] => 48
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,2,3,2] => 288
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,2,3] => 192
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => 384
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,2,1,1,1] => 192
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => 48
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,5,1] => 40
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,1,2,1,1,1] => 32
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,8] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,7,1] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,6,2] => 21
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,6,1,1] => 21
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,5,3] => 35
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,4,4] => 35
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => 35
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,5] => 21
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,3,1,1] => 126
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1] => 21
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,6] => 7
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,5,1] => 35
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,2,4] => 35
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2,2] => 105
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,1,2,1,1] => 21
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,1,2] => 7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,7] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,6,1] => 6
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,3,2,2] => 45
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1] => 15
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,2,5] => 6
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,1,2] => 6
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1,1] => 6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,6] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,3,1,1,1] => 10
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,2,4] => 5
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2,2] => 15
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,5] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,4,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,3,1,1] => 6
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,2,3] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,2,1,2] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,2,1,1,1] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,4] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,3,1] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,2,2] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,2,1,1] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,7] => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,2,3] => 192
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,2,1] => 384
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,1,1,2] => 8
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,8] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,7,1] => 7
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2,2] => 105
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1,1,1] => 7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,7] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,2,1,1,1,2] => 6
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1,1,1] => 6
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,6] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,5,1] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2,2] => 15
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,2,1,1,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,5] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,2,1,1,1] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,4] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,1,2,2] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,1,2,1,1] => 3
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [9] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,6] => 28
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => 56
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => 70
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => 56
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => 28
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,8] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7] => 8
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [9] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [9] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [9] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,3] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,5] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,6] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,7] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => 8
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,8] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [9] => 1
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 56
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 70
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 56
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,1,1] => 28
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => 8
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => 8
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => 28
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 56
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [9] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,8] => 1
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => 35
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [5,2,1,1] => 210
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,6] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,4] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,4] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,5] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,5] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,6] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,7] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,7] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,8] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,6] => 28
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,4,1] => 4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,1,4] => 7
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,2,5] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [9] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [9] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,8] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [8,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => 28
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => 56
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => 70
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => 56
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2,2] => 420
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => 210
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [7,2] => 28
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,1] => 8
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => 112
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => 448
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [7,2] => 28
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [9] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [9] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [6,3] => 56
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [4,4,1] => 224
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,7,1] => 7
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [9] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => [7,2] => 28
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 70
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => 56
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [7,1,1] => 28
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,1] => 8
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,7] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,6] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [9] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,1] => 8
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => 56
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,6] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [9] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [9] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,1] => 8
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,1] => 8
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,1] => 8
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [9] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [9] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [9] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0] => [4,4,1] => 224
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [9] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [9] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => 8
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,1] => 8
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,1,4] => 7
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,1,1,3] => 21
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,4,2] => 70
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => 448
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,1] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [9] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 56
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 70
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [9] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [9] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,8] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,8] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [9] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [9] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => 210
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [9] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [9] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [9] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [9] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7] => 8
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => 28
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,6] => 28
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,7] => 8
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,7] => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,2,4] => 35
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => 112
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => 210
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,1,1,1] => 84
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0] => [9] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0] => [9] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,7] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [7,2] => 28
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [9] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,8] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => 56
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,4] => 70
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0] => [6,3] => 56
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => 70
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,8] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [9] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => 70
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [9] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [9] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [9] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [7,1,1] => 28
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [9] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,4] => 6
[1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [9] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => 105
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,6,2] => 21
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,8] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,5,2,1] => 70
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,8] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,5,3] => 35
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,4,1] => 84
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => 448
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [9] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [9] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [7,2] => 28
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => 8
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,6] => 28
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => 28
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,8] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [9] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [9] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0] => [9] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,5] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,2,3] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [9] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,8] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,4] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,5] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,3] => 192
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,5] => 48
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,7] => 8
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,8] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,6] => 7
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,2,3] => 192
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,5] => 48
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,2,7] => 8
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0] => [9] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0] => [5,4] => 70
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,5] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [7,1,1] => 28
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,7] => 8
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,8] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7] => 8
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,6] => 28
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0] => [5,4] => 70
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => 210
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4] => 120
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [9] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [8,1] => 8
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0] => [8,1] => 8
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [4,2,1,1,1] => 224
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,1,1,1] => 140
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,8] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [9] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,1] => 8
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => 1
[1,1,1,0,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,6,1] => 6
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,1,3,1] => 21
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,2,4] => 5
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [9] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3] => 160
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,4,1] => 192
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5] => 56
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,8] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => 56
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => 112
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [9] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [9] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,8] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [7,1,1] => 28
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [9] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [9] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,7] => 8
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [9] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [9] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => 112
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0] => [8,1] => 8
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => 105
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => 210
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,3,1,1,2] => 15
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [9] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => 112
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,2] => 28
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,8] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,1,4] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,7] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0] => [9] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => 28
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => 105
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,6,2] => 21
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [9] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,5] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => 112
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,7] => 8
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => 1
[1,0,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 28
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,7,1] => 7
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [9] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0] => [9] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => 56
[1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0] => [9] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,6,1] => 6
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,2] => 28
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [9] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [8,1] => 8
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [8,1] => 8
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [9] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,1,1] => 21
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,6,2] => 21
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => 8
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,1] => 8
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [9] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,7] => 1
[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,8] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,8] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => 112
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => 210
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,1] => 8
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,8] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,8] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [9] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,3,4] => 15
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,2] => 70
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0] => [6,3] => 56
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => 8
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,3,1,1,1,2] => 21
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3] => 35
[1,0,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 56
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [9] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,3] => 56
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,7] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,4,2] => 280
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,6] => 28
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [9] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5] => 21
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => 210
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [9] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [4,4,1] => 224
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => 112
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,8] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,6] => 7
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [9] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,1,4] => 7
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,1,8] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0] => [4,5] => 56
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,6] => 28
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => 448
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,5] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,5] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,7] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,6] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,5] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3] => 280
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,6,2] => 21
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0] => [9] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,8] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,6] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,6] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,7] => 1
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => 35
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [9] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,8] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,8] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,6] => 28
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => 28
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,2] => 28
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0] => [6,3] => 56
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0] => [7,2] => 28
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,6,1] => 6
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 9,1,4 23,1,4,9,0,4,0,1 65,1,4,9,23,4,0,1,0,19,0,0,0,0,4,0,0,0,0,2 197,1,4,9,23,69,0,1,0,19,0,1,0,0,50,0,0,4,0,22,0,0,0,9,0,0,0,0,0,2,0,0,0,0,0,4,0,0,0,5,0,0,0,0,8,0,0,1
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 4\ q + q^{2}$
$F_{4} = 9\ q + q^{2} + 4\ q^{3}$
$F_{5} = 23\ q + q^{2} + 4\ q^{3} + 9\ q^{4} + 4\ q^{6} + q^{8}$
$F_{6} = 65\ q + q^{2} + 4\ q^{3} + 9\ q^{4} + 23\ q^{5} + 4\ q^{6} + q^{8} + 19\ q^{10} + 4\ q^{15} + 2\ q^{20}$
$F_{7} = 197\ q + q^{2} + 4\ q^{3} + 9\ q^{4} + 23\ q^{5} + 69\ q^{6} + q^{8} + 19\ q^{10} + q^{12} + 50\ q^{15} + 4\ q^{18} + 22\ q^{20} + 9\ q^{24} + 2\ q^{30} + 4\ q^{36} + 5\ q^{40} + 8\ q^{45} + q^{48}$
Description
The number of standard immaculate tableaux of a given shape.
See Proposition 3.13 of [2] for a hook-length counting formula of these tableaux.
See Proposition 3.13 of [2] for a hook-length counting formula of these tableaux.
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Lalanne-Kreweras involution
Description
The Lalanne-Kreweras involution on Dyck paths.
Label the upsteps from left to right and record the labels on the first up step of each double rise. Do the same for the downsteps. Then form the Dyck path whose ascent lengths and descent lengths are the consecutives differences of the labels.
Label the upsteps from left to right and record the labels on the first up step of each double rise. Do the same for the downsteps. Then form the Dyck path whose ascent lengths and descent lengths are the consecutives differences of the labels.
Map
touch composition
Description
Sends a Dyck path to its touch composition given by the composition of lengths of its touch points.
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