Identifier
-
Mp00027:
Dyck paths
—to partition⟶
Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
St000920: Dyck paths ⟶ ℤ
Values
[1,0] => [] => [] => [1,0] => 1
[1,0,1,0] => [1] => [1,0] => [1,1,0,0] => 1
[1,1,0,0] => [] => [] => [1,0] => 1
[1,0,1,0,1,0] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[1,0,1,1,0,0] => [1,1] => [1,1,0,0] => [1,1,1,0,0,0] => 2
[1,1,0,0,1,0] => [2] => [1,0,1,0] => [1,1,0,1,0,0] => 1
[1,1,0,1,0,0] => [1] => [1,0] => [1,1,0,0] => 1
[1,1,1,0,0,0] => [] => [] => [1,0] => 1
[1,0,1,0,1,0,1,0] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,0,0] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,0] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,0] => [1,1,1] => [1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,0] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,0] => [2,2] => [1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,0] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[1,1,0,1,1,0,0,0] => [1,1] => [1,1,0,0] => [1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,0] => [3] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,0] => [2] => [1,0,1,0] => [1,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,0] => [1] => [1,0] => [1,1,0,0] => 1
[1,1,1,1,0,0,0,0] => [] => [] => [1,0] => 1
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,0] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,0] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,0] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,0] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0] => [2,2] => [1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0] => [1,1] => [1,1,0,0] => [1,1,1,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,0] => [4] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0] => [3] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,0] => [2] => [1,0,1,0] => [1,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0] => [1] => [1,0] => [1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0] => [] => [] => [1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
>>> Load all 741 entries. <<<[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [1,1,0,0] => [1,1,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => [1,0,1,0] => [1,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [1] => [1,0] => [1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [] => [] => [1,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [1,1,0,0] => [1,1,1,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => [1,0,1,0] => [1,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => [1,0] => [1,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [] => [] => [1,0] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => 3
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 3
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 3
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 3
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,6] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [1,1,0,0] => [1,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [1,0,1,0] => [1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => [1,0] => [1,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [] => [] => [1,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,4] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,5] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,6] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [8,7] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,8] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [7,7,2] => [1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,2,2,2] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => 2
[] => [] => [] => [1,0] => 1
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 3
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 3
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,5,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => [1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,5] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => [1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => [1,1,0,0] => [1,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => [1,0,1,0] => [1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => [1,0] => [1,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [] => [] => [1,0] => 1
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4,4,4] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,5,5,5,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [] => [] => [1,0] => 1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => [1,1,0,0] => [1,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => [1,0,1,0] => [1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => [1,1,0,0] => [1,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => [1,0,1,0] => [1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => [1,0] => [1,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => [1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => [1,0] => [1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,4,4,4] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,5,5] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => [1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,5,5,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [] => [] => [1,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [7,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [7,7] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,6,6,6,6] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1] => [1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,5,5,5,5,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 3
[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => 3
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => [1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [3] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => [1,1,0,0] => [1,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
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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:
3,2 4,10 5,37
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 3\ q + 2\ q^{2}$
$F_{4} = 4\ q + 10\ q^{2}$
$F_{5} = 5\ q + 37\ q^{2}$
Description
The logarithmic height of a Dyck path.
This is the floor of the binary logarithm of the usual height increased by one:
$$ \lfloor\log_2(1+height(D))\rfloor $$
This is the floor of the binary logarithm of the usual height increased by one:
$$ \lfloor\log_2(1+height(D))\rfloor $$
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
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