Identifier
-
Mp00296:
Dyck paths
—Knuth-Krattenthaler⟶
Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001068: Dyck paths ⟶ ℤ (values match St000015The number of peaks of a Dyck path., St000053The number of valleys of the Dyck path., St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra.)
Values
[1,1,0,0] => [1,0,1,0] => [1] => [1,0,1,0] => 2
[1,0,1,1,0,0] => [1,1,0,1,0,0] => [1] => [1,0,1,0] => 2
[1,1,0,0,1,0] => [1,0,1,0,1,0] => [2,1] => [1,0,1,0,1,0] => 3
[1,1,0,1,0,0] => [1,0,1,1,0,0] => [1,1] => [1,0,1,1,0,0] => 2
[1,1,1,0,0,0] => [1,1,0,0,1,0] => [2] => [1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [1] => [1,0,1,0] => 2
[1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0] => [2,1] => [1,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => [1,1] => [1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => [2] => [1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 2
[1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0] => [3,1] => [1,1,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0] => [3,2] => [1,1,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0] => [3] => [1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => [1] => [1,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => [1,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => [2] => [1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => [3] => [1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1] => [1,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => [1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 3
>>> Load all 1104 entries. <<<[1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => [1,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [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] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 5
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 5
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 6
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 5
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 4
[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] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 5
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 5
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 5
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 5
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 5
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 6
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 5
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 5
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 5
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 5
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 5
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 5
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 5
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 5
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 5
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 5
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 5
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 4
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 5
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [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] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 5
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 6
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 6
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 5
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 5
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 5
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 5
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 5
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 5
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 5
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 5
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
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Description
Number of torsionless simple modules in the corresponding Nakayama algebra.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition λ associated to a Dyck path is defined to be the complementary partition inside the staircase partition (n−1,…,2,1) when cutting out D considered as a path from (0,0) to (n,n).
In other words, λi 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,…,2,1).
The partition λ associated to a Dyck path is defined to be the complementary partition inside the staircase partition (n−1,…,2,1) when cutting out D considered as a path from (0,0) to (n,n).
In other words, λi 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,…,2,1).
Map
Knuth-Krattenthaler
Description
The map that sends the Dyck path to a 321-avoiding permutation, then applies the Robinson-Schensted correspondence and finally interprets the first row of the insertion tableau and the second row of the recording tableau as up steps.
Interpreting a pair of two-row standard tableaux of the same shape as a Dyck path is explained by Knuth in [1, pp. 60].
Krattenthaler's bijection between Dyck paths and 321-avoiding permutations used is Mp00119to 321-avoiding permutation (Krattenthaler), see [2].
This is the inverse of the map Mp00127left-to-right-maxima to Dyck path that interprets the left-to-right maxima of the permutation obtained from Mp00024to 321-avoiding permutation as a Dyck path.
Interpreting a pair of two-row standard tableaux of the same shape as a Dyck path is explained by Knuth in [1, pp. 60].
Krattenthaler's bijection between Dyck paths and 321-avoiding permutations used is Mp00119to 321-avoiding permutation (Krattenthaler), see [2].
This is the inverse of the map Mp00127left-to-right-maxima to Dyck path that interprets the left-to-right maxima of the permutation obtained from Mp00024to 321-avoiding permutation as a Dyck path.
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