Identifier
-
Mp00133:
Integer compositions
—delta morphism⟶
Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001199: Dyck paths ⟶ ℤ
Values
[1,1] => [2] => [1,1,0,0] => [1,0,1,0] => 1
[1,1,1] => [3] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 2
[1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 3
[1,1,2] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[2,1,1] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[2,2] => [2] => [1,1,0,0] => [1,0,1,0] => 1
[1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0] => 2
[1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,3] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[1,2,2] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => 2
[2,2,1] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[3,1,1] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0] => 2
[1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => 1
[1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,4] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 3
[2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => 1
[2,2,2] => [3] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 2
[3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => 2
[3,3] => [2] => [1,1,0,0] => [1,0,1,0] => 1
[4,1,1] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,2,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0] => 2
[1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,2,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[1,1,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,5] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[1,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[1,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => 2
[1,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,3,3] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[1,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[2,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[2,2,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[2,2,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[2,2,2,1] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0] => 2
[2,2,3] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[2,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 3
[3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[3,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[3,2,2] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[3,3,1] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => 2
[5,1,1] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[1,1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,2,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,3] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,2,1,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,1,2,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,3,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,2,1,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,2,1,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,2,2,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,2,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,3,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,3,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,4,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,5] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0] => 2
[1,1,2,1,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,2,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,2,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,2,2,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,2,2,2] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,2,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,2,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,3,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,3,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,3,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,3,3] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => 1
>>> Load all 1448 entries. <<<[1,1,4,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[1,1,4,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,5,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,6] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[1,2,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,2,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,2,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,2,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,2,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,2,2,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,2,2,1,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,2,2,2,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[1,2,2,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[1,2,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,3,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,3,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,3,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,3,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[1,3,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[1,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[2,1,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[2,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[2,1,1,1,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[2,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[2,1,1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[2,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[2,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,1,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[2,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,2,1,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[2,2,1,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[2,2,1,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[2,2,1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[2,2,2,1,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[2,2,2,2] => [4] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 3
[2,2,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[2,2,4] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[2,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,3,3] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[2,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[3,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[3,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[3,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[3,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[3,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[3,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[3,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[3,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[3,3,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => 1
[3,3,2] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[4,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 3
[4,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[4,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[4,2,2] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[4,4] => [2] => [1,1,0,0] => [1,0,1,0] => 1
[5,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => 2
[6,1,1] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[1,1,1,1,1,1,3] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,2,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,3,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,4] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,2,1,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,2,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,2,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,3,1,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,1,3,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,4,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,5] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,2,1,1,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,2,1,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,2,1,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,2,2,1,1] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,2,2,2] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,2,3,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,2,4] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,3,1,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,3,1,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,3,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,3,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,4,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,4,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,5,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,6] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0] => 2
[1,1,2,1,1,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,2,1,1,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,1,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,2,1,2,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,2,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,2,1,3,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,2,2,1,1,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,2,2,1,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,2,2,2,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,2,2,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,2,3,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,2,3,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,2,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,2,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,3,1,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,3,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,3,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,3,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,3,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,3,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[1,1,3,3,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,3,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,4,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,4,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,4,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,4,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,5,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[1,1,5,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,6,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,7] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[1,2,1,1,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,2,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,2,1,1,1,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,2,1,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,2,1,1,2,2] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,2,1,1,3,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,2,1,1,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,2,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,2,1,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,2,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,2,1,1,1,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,2,2,1,1,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,2,2,1,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,2,2,1,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,2,2,2,1,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,2,2,2,2] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 3
[1,2,2,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,2,2,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[1,2,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,2,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[1,2,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,3,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,3,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,3,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,3,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,3,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,3,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,3,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,3,3,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[1,3,3,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[1,4,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,4,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,4,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,4,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[1,4,4] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[1,5,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,6,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[2,1,1,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[2,1,1,1,1,2,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[2,1,1,1,1,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[2,1,1,1,2,1,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[2,1,1,1,2,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 1
[2,1,1,1,3,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,1,1,1,4] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[2,1,1,2,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[2,1,1,2,1,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,1,1,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[2,1,1,2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,1,1,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[2,1,1,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,1,1,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,1,1,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[2,1,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[2,1,2,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[2,1,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[2,1,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,1,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,1,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[2,1,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,2,1,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[2,2,1,1,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[2,2,1,1,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[2,2,1,1,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[2,2,1,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[2,2,1,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[2,2,1,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[2,2,1,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[2,2,2,1,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 2
[2,2,2,1,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[2,2,2,2,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 3
[2,2,2,3] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0] => 2
[2,2,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[2,2,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[2,2,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[2,2,5] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[2,3,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[2,3,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[2,3,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,3,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[2,3,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[2,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[3,1,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[3,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[3,1,1,1,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[3,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[3,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[3,1,1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[3,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[3,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[3,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[3,1,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[3,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[3,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[3,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[3,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => 2
[3,3,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[3,3,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[3,3,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[3,3,3] => [3] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 2
[3,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[4,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[4,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[4,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[4,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[4,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[4,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[4,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[4,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[4,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[4,4,1] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[5,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 3
[5,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[5,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[5,2,2] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[6,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => 2
[7,1,1] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[1,1,1,1,1,1,4] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,2,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,3,2] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,4,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,5] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,2,1,3] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,2,2,2] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,1,2,3,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,2,4] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,3,1,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,3,2,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,3,3] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,4,1,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,1,4,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,5,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,6] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,2,1,1,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,2,1,2,2] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,2,1,3,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,2,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,2,2,1,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,2,2,2,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,2,2,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,2,3,1,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,2,3,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,2,4,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,2,5] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,3,1,1,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,3,1,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,3,1,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,3,2,1,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,3,2,2] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,3,3,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,3,4] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,4,1,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,4,1,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,4,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,4,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,5,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,5,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,6,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,7] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0] => 2
[1,1,2,1,1,1,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,2,1,1,2,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,2,1,1,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,1,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,2,1,2,1,2] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,2,1,2,2,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,2,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,3,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,3,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,4,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,5] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,2,2,1,1,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,2,2,1,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,2,2,1,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,2,2,2,1,1] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,2,2,2,2] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,2,2,3,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,2,2,4] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,2,3,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,2,3,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,3,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,3,3] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[1,1,2,4,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,2,4,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,2,5,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,2,6] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,3,1,1,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,3,1,1,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,1,3,1,1,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,3,1,2,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,3,1,2,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,3,1,3,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,3,1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,3,2,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,3,2,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,3,2,2,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,3,2,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,3,3,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,3,3,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,3,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,3,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,4,1,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,4,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,4,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,4,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,4,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,4,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[1,1,4,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,4,4] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => 1
[1,1,5,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,5,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,5,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,5,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,6,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[1,1,6,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,7,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,8] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[1,2,1,1,1,1,3] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,2,1,1,1,2,2] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,2,1,1,1,3,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,2,1,1,1,4] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,2,1,1,2,1,2] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,1,2,2,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[1,2,1,1,2,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,2,1,1,3,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,2,1,1,3,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,2,1,1,4,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,2,1,1,5] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,2,1,2,1,1,2] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,2,1,2,2,2] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,2,1,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,2,1,3,3] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,2,1,4,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,2,1,1,1,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,2,2,1,1,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[1,2,2,1,1,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,2,2,1,2,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,2,2,1,2,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,2,2,1,3,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,2,2,1,4] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,2,2,2,1,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,2,2,2,1,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,2,2,2,2,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,2,2,2,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[1,2,2,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,2,2,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,2,2,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,2,2,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[1,2,3,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,2,3,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,2,3,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,2,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,2,4,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,2,5,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,3,1,1,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,3,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,3,1,1,1,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,3,1,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,3,1,1,2,2] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,3,1,1,3,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,3,1,1,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,3,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,3,1,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,3,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,3,2,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,3,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,3,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,3,3,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,3,3,1,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,3,3,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,3,3,3] => [1,3] => [1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => 2
[1,3,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,4,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,4,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,4,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,4,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,4,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,4,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,4,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,4,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,4,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,4,4,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[1,5,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,5,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,5,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,5,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[1,6,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,7,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[2,1,1,1,1,1,3] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[2,1,1,1,1,2,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1
[2,1,1,1,1,3,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[2,1,1,1,1,4] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[2,1,1,1,2,1,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[2,1,1,1,2,2,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1
[2,1,1,1,2,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,1,1,1,3,1,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[2,1,1,1,3,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,1,1,1,4,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,1,1,1,5] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[2,1,1,2,1,1,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1
[2,1,1,2,1,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,1,1,2,1,3] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,1,1,2,2,1,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1
[2,1,1,2,2,2] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[2,1,1,2,3,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,1,1,2,4] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,1,1,3,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[2,1,1,3,1,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,1,1,3,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,1,1,3,3] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[2,1,1,4,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[2,1,1,4,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,1,1,5,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,1,1,6] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[2,1,2,1,1,1,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,1,2,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,1,2,1,1,3] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[2,1,2,1,2,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,1,2,1,2,2] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,2,2,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[2,1,2,2,1,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,1,2,2,2,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[2,1,2,2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[2,1,2,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[2,1,3,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,1,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[2,1,4,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,1,5,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,2,1,1,1,1,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1
[2,2,1,1,1,2,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[2,2,1,1,1,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[2,2,1,1,2,1,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1
[2,2,1,1,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,2,1,1,3,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[2,2,1,1,4] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[2,2,1,2,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[2,2,1,2,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,2,1,2,2,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[2,2,1,2,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[2,2,1,3,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[2,2,1,3,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[2,2,1,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[2,2,1,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[2,2,2,1,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[2,2,2,1,1,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[2,2,2,1,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[2,2,2,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[2,2,2,2,1,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[2,2,2,2,2] => [5] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[2,2,2,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[2,2,2,4] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0] => 2
[2,2,3,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[2,2,3,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[2,2,3,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[2,2,3,3] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => 1
[2,2,4,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[2,2,4,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[2,2,5,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[2,2,6] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[2,3,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[2,3,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[2,3,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,3,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[2,3,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,3,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,3,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,3,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[2,3,3,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[2,3,3,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[2,4,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[2,4,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[2,4,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,4,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[2,4,4] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[2,5,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,6,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[3,1,1,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[3,1,1,1,1,2,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[3,1,1,1,1,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[3,1,1,1,2,1,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[3,1,1,1,2,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 1
[3,1,1,1,3,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[3,1,1,1,4] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[3,1,1,2,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[3,1,1,2,1,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[3,1,1,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[3,1,1,2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[3,1,1,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[3,1,1,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[3,1,1,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[3,1,1,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[3,1,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[3,1,2,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[3,1,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[3,1,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[3,1,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[3,1,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[3,1,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[3,2,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[3,2,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[3,2,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[3,2,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[3,2,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[3,2,2,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[3,2,2,1,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[3,2,2,2,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[3,2,2,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[3,2,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[3,3,1,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[3,3,1,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[3,3,1,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[3,3,1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[3,3,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[3,3,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => 1
[3,3,3,1] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0] => 2
[3,3,4] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[3,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[3,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[4,1,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[4,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[4,1,1,1,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[4,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[4,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[4,1,1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[4,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[4,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[4,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[4,1,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[4,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[4,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[4,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[4,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[4,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => 2
[4,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[4,3,3] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[4,4,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => 1
[4,4,2] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[5,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[5,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[5,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[5,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[5,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[5,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[5,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[5,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[5,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[5,5] => [2] => [1,1,0,0] => [1,0,1,0] => 1
[6,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 3
[6,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[6,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[6,2,2] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[7,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => 2
[8,1,1] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[1,8,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[1,1,8,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,1,1,4,4] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,2,3,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,2,1,3,4] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,3,3,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,3,2,2,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,3,1,2,4] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,4,4,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,4,3,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,4,2,1,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,4,1,1,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,5,5] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => 1
[2,2,1,1,3,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,2,2,2,2,2] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[2,2,2,1,2,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[2,2,3,3,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,2,3,2,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,2,3,1,1,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[2,2,4,4] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => 1
[2,1,1,2,3,3] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[2,1,1,1,3,4] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,1,2,3,2,2] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,2,2,2,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[2,1,3,4,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,3,1,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,1,3,1,1,4] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[3,3,1,1,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,3,2,2,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,3,2,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[3,3,3,3] => [4] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 3
[3,2,1,2,2,2] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[3,2,1,1,2,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[3,2,2,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[3,2,2,2,1,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[3,2,2,1,1,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[3,1,1,3,2,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[3,1,1,2,2,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[3,1,1,1,2,4] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[3,1,2,4,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[3,1,2,2,1,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[3,1,2,1,1,4] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[4,4,1,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[4,4,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => 1
[4,3,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[4,3,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[4,2,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[4,2,1,1,1,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[4,2,2,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[4,1,1,4,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[4,1,1,3,1,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[4,1,1,2,1,3] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[4,1,1,1,1,4] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[5,5,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => 1
[5,1,1,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[6,6] => [2] => [1,1,0,0] => [1,0,1,0] => 1
[1,2,2,2,2,2,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,2,2,2,3,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,2,2,3,3,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,2,2,3,2,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,2,2,4,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,2,3,3,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,2,3,2,2,2] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,2,3,3,3] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,2,4,4,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,3,3,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,3,3,3,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[1,3,4,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,3,2,2,3,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,3,2,2,2,2] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,3,2,3,3] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,3,3,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,3,3,2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,3,4,4] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[1,4,4,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,4,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,4,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,4,4,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[1,4,2,2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,5,5,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[1,5,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[2,3,2,2,2,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[2,3,3,3,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[2,3,3,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[2,4,4,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[2,4,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,4,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[2,2,3,2,2,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[2,2,3,3,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[2,2,4,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[2,2,4,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[2,2,5,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[2,2,2,3,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[2,2,2,4,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[2,2,2,2,3,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[2,2,2,3,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[2,2,3,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[2,2,3,2,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[2,3,2,2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[2,3,3,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[2,5,5] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[3,4,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[3,5,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[3,3,3,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[3,3,4,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[3,3,2,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[3,3,2,2,2] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[3,4,4,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[3,2,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[3,2,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[3,2,2,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[3,2,2,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[3,2,2,2,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[3,3,5,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[3,3,2,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[4,4,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[4,3,3,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[4,4,4] => [3] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 2
[4,2,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[5,5,2] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[1,6,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,5,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,4,1,1,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,6,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[1,7,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,6,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,4,2,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,5,1,1,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,3,2,1,1,1,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,2,2,2,2,2] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[1,2,2,2,1,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,2,2,1,3,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,2,2,1,2,3] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,2,2,1,1,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,2,1,3,2,2] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,1,2,2,3] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,2,1,1,4,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,2,1,1,3,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,2,1,1,2,4] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,2,1,1,1,5] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,1,3,2,2,2] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,3,2,1,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,3,1,3,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,3,1,2,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,3,1,1,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,2,3,2,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,2,3,1,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,2,3,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,2,2,2,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,2,2,1,4] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,2,1,4,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,3,3] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,2,1,2,4] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,1,5] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,4,2,2] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,4,1,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,3,3,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,3,2,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,3,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,2,4,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,2,3,3] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,2,2,4] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,2,1,5] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,5,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,4,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,3,4] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,2,5] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,1,6] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,2,2,2,2,2,2] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,2,2,2,2,1,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,2,2,2,1,3,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,2,2,2,1,2,3] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,2,2,2,1,1,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,2,2,1,3,2,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,2,2,1,3,1,3] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,2,2,1,2,3,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,2,2,1,2,2,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1
[1,2,2,1,2,1,4] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,2,2,1,1,4,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[1,2,2,1,1,3,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1
[1,2,2,1,1,2,4] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[1,2,2,1,1,1,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,2,1,3,2,2,2] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,2,1,3,1,1,4] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,2,3,2,2] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,2,2,3,2] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,2,2,2,3] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,2,1,2,2,1,4] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,2,1,3,3] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,2,1,1,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,1,4,2,2] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,2,1,1,4,1,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,1,3,3,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[1,2,1,1,3,2,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,1,3,1,4] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,1,2,4,2] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,1,2,3,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,2,1,1,2,2,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[1,2,1,1,2,1,5] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,1,1,5,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,2,1,1,1,4,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,2,1,1,1,3,4] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,2,1,1,1,2,5] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,2,1,1,1,1,6] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,3,2,2,2,2] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,3,2,2,1,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,1,3,2,1,3,2] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,3,2,1,2,3] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,3,2,1,1,4] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,3,1,3,2,2] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,3,1,3,1,3] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,3,1,2,3,2] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,3,1,2,2,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,3,1,2,1,4] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,3,1,1,4,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,1,3,1,1,3,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,3,1,1,2,4] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,1,3,1,1,1,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,2,3,2,2,2] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,2,3,2,1,3] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,2,3,1,3,2] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,2,3,1,2,3] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,2,3,1,1,4] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,2,3,2,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,2,2,3,1,3] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,2,2,2,3,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,2,2,2,2,3] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,2,2,2,1,4] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,2,2,1,4,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,2,2,1,3,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,2,2,1,2,4] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,2,2,1,1,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,2,1,4,2,2] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,4,1,3] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,2,1,3,3,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,3,2,3] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,2,1,3,1,4] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,2,1,2,4,2] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,2,1,2,3,3] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,2,2,4] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,2,1,5] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,2,1,1,5,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,1,4,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,1,3,4] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,1,2,5] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,1,1,6] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,4,2,2,2] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,4,2,1,3] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,4,1,3,2] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,4,1,2,3] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,4,1,1,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,3,3,2,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,3,3,1,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,3,2,3,2] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,3,2,2,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,3,2,1,4] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,3,1,4,2] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,3,1,3,3] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,3,1,2,4] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,3,1,1,5] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,2,4,2,2] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,2,4,1,3] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,2,3,3,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,2,3,2,3] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,2,3,1,4] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,2,2,4,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,2,2,3,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,2,2,2,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,2,2,1,5] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,2,1,5,2] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,2,1,4,3] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,2,1,3,4] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,2,1,2,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,2,1,1,6] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,5,2,2] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,1,5,1,3] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,4,3,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,4,2,3] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,4,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,3,4,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,3,3,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,1,3,2,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,3,1,5] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,2,5,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,2,4,3] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,2,3,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,2,2,5] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,2,1,6] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,1,6,2] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,5,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,4,4] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,3,5] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,2,6] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,7] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,2,1,7] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,2,2,2,5] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[1,1,2,3,5] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,4,1,5] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,2,1,1,5] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,2,1,2,2,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,5,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[3,1,2,3,3] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,4,3,3] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,2,1,3,3] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,2,2,1,2,1,3] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,3,2,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,2,2,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,6,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,2,3,1,3] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[3,1,1,2,1,1,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1
[1,3,1,2,1,1,3] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,3,2,1,1,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,4,1,1,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,2,1,4,2,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[5,2,2,2,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[1,6,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,1,2,3,2,2,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[3,1,2,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,4,1,2,2,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,2,1,2,4,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,2,2,6,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,1,2,7,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,4,5,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,2,1,5,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,2,2,1,2,3,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,2,2,2,3,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,6,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,2,3,3,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[3,1,1,2,1,3,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,3,2,1,3,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,4,1,3,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[7,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,2,4,1,2,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,2,2,1,2,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,4,2,1,2,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[5,3,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,2,2,3,2,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[3,5,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,7,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,2,4,2,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,1,2,2,2,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,3,2,2,2,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,4,2,2,1,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1
[5,1,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,2,2,1,4,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[3,3,4,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[1,5,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,2,2,4,1,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1
[3,1,6,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,3,6,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,8,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,2,5,1,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[3,1,1,2,3,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,3,1,2,3,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,3,2,3,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,4,3,1,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[5,1,1,2,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[3,3,1,2,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,5,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[3,1,3,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,3,3,2,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,5,2,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[3,1,1,4,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,3,1,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,3,4,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,6,1,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[2,2,2,2,1,2,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[2,2,2,1,2,1,2] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[2,2,2,1,2,2,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[2,2,2,1,1,2,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[2,2,1,2,1,2,2] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,2,1,2,2,1,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[2,2,1,2,2,2,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1
[2,2,1,1,2,2,2] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[2,1,2,1,2,2,2] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,2,2,1,2,2] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,1,2,2,2,1,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[2,1,2,2,2,2,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[2,1,1,2,2,2,2] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,2,1,2,2,2,2] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,2,2,1,2,2,2] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,2,2,2,1,2,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,2,2,2,2,1,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,2,2,2,2,2] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[3,3,3,2] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0] => 2
[3,4,4] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[2,3,3,3] => [1,3] => [1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => 2
[4,4,3] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[3,2,2,2,2,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[4,3,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[4,2,2,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[4,2,2,2,2] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 3
[5,3,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[5,3,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[5,2,2,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[6,3,3] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[2,1,1,6,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,1,1,1,5,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,1,1,1,1,4,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[2,2,6,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[2,1,1,7,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,1,1,1,6,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,1,1,2,4,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,1,1,1,1,5,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[2,1,1,1,2,3,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[2,2,2,2,2,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[3,1,2,2,2,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[2,3,1,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[3,2,1,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[4,1,1,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[2,2,3,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,2,2,1,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,4,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[3,3,1,1,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[4,2,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[5,1,1,1,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,2,2,3,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 1
[3,1,2,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,3,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[3,2,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[4,1,1,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[2,2,3,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[3,1,3,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,3,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[3,2,2,2,1,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 1
[4,1,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[2,4,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[3,3,1,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[4,2,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[5,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[2,2,4,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[3,1,4,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,3,3,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[3,2,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[4,1,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,4,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[3,3,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[4,2,2,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[5,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,5,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[3,4,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[4,3,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[5,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[6,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[2,2,2,2,2,2,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[3,1,2,2,2,2,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[2,3,1,2,2,2,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[3,2,1,2,2,2,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[4,1,1,2,2,2,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1
[2,2,3,1,2,2,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[3,1,3,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,2,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,2,2,1,2,2,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1
[4,1,2,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,1,2,2,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[3,3,1,1,2,2,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[4,2,1,1,2,2,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[5,1,1,1,2,2,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1
[2,2,2,3,1,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[4,1,1,3,1,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,2,3,2,1,2,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,3,2,2,1,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,2,2,2,1,2,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[4,1,2,2,1,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,3,1,2,1,2,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[5,1,1,2,1,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[2,2,4,1,1,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[3,1,4,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,3,1,1,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[3,2,3,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[4,1,3,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,2,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[3,3,2,1,1,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[4,2,2,1,1,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[5,1,2,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,4,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[4,3,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[5,2,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[6,1,1,1,1,2,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[2,2,2,2,3,1,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1
[3,1,2,2,3,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,3,1,2,3,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,2,1,2,3,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[4,1,1,2,3,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,2,3,1,3,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,1,3,1,3,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,2,1,3,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,2,2,1,3,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[4,1,2,1,3,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,1,3,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[3,3,1,1,3,1,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1
[4,2,1,1,3,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[5,1,1,1,3,1,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[2,2,2,3,2,1,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[3,1,2,3,2,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,1,3,2,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,2,1,3,2,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[4,1,1,3,2,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,2,3,2,2,1,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1
[3,1,3,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[2,3,2,2,2,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[3,2,2,2,2,1,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1
[4,1,2,2,2,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[2,4,1,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[3,3,1,2,2,1,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1
[4,2,1,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[5,1,1,2,2,1,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1
[2,2,4,1,2,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,1,4,1,2,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,3,1,2,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[3,2,3,1,2,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[4,1,3,1,2,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,2,1,2,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,3,2,1,2,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[4,2,2,1,2,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[5,1,2,1,2,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,5,1,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[3,4,1,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[4,3,1,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[5,2,1,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[6,1,1,1,2,1,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[2,2,2,4,1,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[3,1,2,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,3,1,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[3,2,1,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[4,1,1,4,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[2,2,3,3,1,1,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[3,1,3,3,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[2,3,2,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[3,2,2,3,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[4,1,2,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,4,1,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[3,3,1,3,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[4,2,1,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[5,1,1,3,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[2,2,4,2,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[3,1,4,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,3,3,2,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[3,2,3,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[4,1,3,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,4,2,2,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[3,3,2,2,1,1,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,2,2,2,1,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[5,1,2,2,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[2,5,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[3,4,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[4,3,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[5,2,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[6,1,1,2,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[2,2,5,1,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1
[3,1,5,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[2,3,4,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[3,2,4,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[4,1,4,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[2,4,3,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[3,3,3,1,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[4,2,3,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[5,1,3,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[2,5,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[3,4,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[4,3,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[5,2,2,1,1,1,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[6,1,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[2,6,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[3,5,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[4,4,1,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,3,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[6,2,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[7,1,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,2,2,4,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,2,4,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,4,2,2,2,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,5,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,5,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[2,6,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[2,2,5,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[6,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => 2
[2,2,2,2,2,1,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,2,2,2,3,1,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,2,2,3,1,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,2,2,4,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,2,3,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,1,3,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,2,3,3,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,2,4,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,2,5,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,3,1,2,2,2,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,3,1,3,2,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,1,3,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,1,1,2,2,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[1,4,1,1,3,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,3,2,2,1,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,3,3,1,1,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[1,4,2,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,5,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,3,2,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,3,3,1,2,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,3,4,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,4,1,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,4,1,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,5,1,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,4,2,2,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,4,3,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,5,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,6,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[2,1,2,2,3,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,1,2,3,2,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,1,2,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,3,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,1,3,1,3,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,1,4,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,1,3,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,3,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[2,1,4,1,2,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,1,4,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,5,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[2,2,1,2,3,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,2,1,3,1,2,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[2,2,1,3,2,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,2,1,4,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[3,1,1,2,2,2,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1
[3,1,1,3,1,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,1,1,3,2,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,2,2,1,3,1,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[2,3,1,1,2,2,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[2,3,1,1,3,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[3,1,2,1,3,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,2,1,1,2,2,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[3,2,1,1,3,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[4,1,1,1,2,2,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1
[4,1,1,1,3,1,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[2,2,3,1,1,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[2,3,2,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[3,1,2,2,1,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[3,1,3,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[4,1,1,2,1,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[3,2,2,1,1,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[3,3,1,1,1,2,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[4,1,2,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[4,2,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[5,1,1,1,1,2,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[2,2,2,3,1,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[2,2,3,1,2,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,2,3,2,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[2,2,4,1,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1
[2,3,1,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[2,3,1,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,3,2,1,2,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,3,2,2,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[2,3,3,1,1,1,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[2,4,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,4,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[2,5,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[3,1,2,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[3,1,3,1,2,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,1,4,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[3,2,1,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[3,2,1,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[4,1,1,2,2,1,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1
[4,1,1,3,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[3,3,1,1,2,1,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1
[4,1,2,1,2,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[4,2,1,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[5,1,1,1,2,1,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[3,2,2,2,1,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[3,2,3,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[3,3,2,1,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1
[3,4,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[4,1,2,2,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[4,1,3,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[4,2,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[4,2,2,1,1,1,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[4,3,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[5,1,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[5,2,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[6,1,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,2,2,4,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,3,1,1,1,5,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,2,3,1,1,4,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,2,3,2,2,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1
[1,2,2,1,4,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,2,2,1,2,4,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,2,1,3,3,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,1,5,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,1,3,4,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,1,1,6,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,5,1,3,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,4,3,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,4,1,4,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,3,1,5,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,2,5,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,2,3,4,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,2,1,6,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,7,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,2,3,2,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,2,2,2,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,2,2,2,2,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,2,2,3,4] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,2,3,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,3,2,2,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[5,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,1,1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,3,1,3,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,5,1,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,7,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,4,1,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,2,1,4,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,2,3,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,3,1,1,1,3,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,3,1,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,5,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,7,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,4,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,4,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,2,1,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,2,1,1,1,4,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,2,1,1,3,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,2,3,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,2,1,2,2,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,7,1,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,9,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,6,1,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,3,1,5,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,5,1,1,1,3,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,5,1,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,7,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,9,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,6,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,6,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,4,1,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,4,1,1,1,4,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,4,1,1,3,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,4,3,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,4,3,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,4,2,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,6,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,2,3,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,2,3,3,1,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,2,5,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,2,5,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,4,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,9] => [2,1] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 1
[2,2,2,2,1,1,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,2,2,1,2,3] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,2,2,2,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[2,2,2,6] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0] => 2
[2,2,6,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,5,5] => [1,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 1
[1,2,2,2,4,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,2,2,5,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,2,2,5,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,1,2,2,2,2,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,2,2,3,1,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,2,3,2,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,3,2,2,1,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1
[1,2,2,2,2,1,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,2,2,2,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,2,5,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,5,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,4,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
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Description
The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
delta morphism
Description
Apply the delta morphism to an integer composition.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
Map
zeta map
Description
The zeta map on Dyck paths.
The zeta map $\zeta$ is a bijection on Dyck paths of semilength $n$.
It was defined in [1, Theorem 1], see also [2, Theorem 3.15] and sends the bistatistic (area, dinv) to the bistatistic (bounce, area). It is defined by sending a Dyck path $D$ with corresponding area sequence $a=(a_1,\ldots,a_n)$ to a Dyck path as follows:
The zeta map $\zeta$ is a bijection on Dyck paths of semilength $n$.
It was defined in [1, Theorem 1], see also [2, Theorem 3.15] and sends the bistatistic (area, dinv) to the bistatistic (bounce, area). It is defined by sending a Dyck path $D$ with corresponding area sequence $a=(a_1,\ldots,a_n)$ to a Dyck path as follows:
- First, build an intermediate Dyck path consisting of $d_1$ north steps, followed by $d_1$ east steps, followed by $d_2$ north steps and $d_2$ east steps, and so on, where $d_i$ is the number of $i-1$'s within the sequence $a$.
For example, given $a=(0,1,2,2,2,3,1,2)$, we build the path
$$NE\ NNEE\ NNNNEEEE\ NE.$$ - Next, the rectangles between two consecutive peaks are filled. Observe that such the rectangle between the $k$th and the $(k+1)$st peak must be filled by $d_k$ east steps and $d_{k+1}$ north steps. In the above example, the rectangle between the second and the third peak must be filled by $2$ east and $4$ north steps, the $2$ being the number of $1$'s in $a$, and $4$ being the number of $2$'s. To fill such a rectangle, scan through the sequence a from left to right, and add east or north steps whenever you see a $k-1$ or $k$, respectively. So to fill the $2\times 4$ rectangle, we look for $1$'s and $2$'s in the sequence and see $122212$, so this rectangle gets filled with $ENNNEN$.
The complete path we obtain in thus
$$NENNENNNENEEENEE.$$
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