Identifier
-
Mp00133:
Integer compositions
—delta morphism⟶
Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001198: Dyck paths ⟶ ℤ (values match St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$.)
Values
[1,1,2] => [2,1] => [1,1] => [1,0,1,0] => 2
[2,1,1] => [1,2] => [1,1] => [1,0,1,0] => 2
[1,1,1,2] => [3,1] => [1,1] => [1,0,1,0] => 2
[1,1,2,1] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,3] => [2,1] => [1,1] => [1,0,1,0] => 2
[1,2,1,1] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[1,2,2] => [1,2] => [1,1] => [1,0,1,0] => 2
[2,1,1,1] => [1,3] => [1,1] => [1,0,1,0] => 2
[2,2,1] => [2,1] => [1,1] => [1,0,1,0] => 2
[3,1,1] => [1,2] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,2] => [4,1] => [1,1] => [1,0,1,0] => 2
[1,1,1,2,1] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,3] => [3,1] => [1,1] => [1,0,1,0] => 2
[1,1,2,1,1] => [2,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,3,1] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,4] => [2,1] => [1,1] => [1,0,1,0] => 2
[1,2,1,1,1] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[1,2,2,1] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,3,1,1] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[2,1,1,1,1] => [1,4] => [1,1] => [1,0,1,0] => 2
[2,1,1,2] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,1,1,1] => [1,3] => [1,1] => [1,0,1,0] => 2
[4,1,1] => [1,2] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,1,2] => [5,1] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,2,1] => [4,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,3] => [4,1] => [1,1] => [1,0,1,0] => 2
[1,1,1,2,1,1] => [3,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,2,2] => [3,2] => [1,1] => [1,0,1,0] => 2
[1,1,1,3,1] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,4] => [3,1] => [1,1] => [1,0,1,0] => 2
[1,1,2,1,1,1] => [2,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,2,1,2] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,2,2,1] => [2,2,1] => [2,1] => [1,1,0,0,1,0] => 2
[1,1,2,3] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,3,1,1] => [2,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,3,2] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,4,1] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,5] => [2,1] => [1,1] => [1,0,1,0] => 2
[1,2,1,1,1,1] => [1,1,4] => [2,1] => [1,1,0,0,1,0] => 2
[1,2,1,1,2] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,2,2,1,1] => [1,2,2] => [1,2] => [1,0,1,1,0,0] => 2
[1,2,2,2] => [1,3] => [1,1] => [1,0,1,0] => 2
[1,3,1,1,1] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[1,3,3] => [1,2] => [1,1] => [1,0,1,0] => 2
[1,4,1,1] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[2,1,1,1,1,1] => [1,5] => [1,1] => [1,0,1,0] => 2
[2,1,1,1,2] => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,1,2,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,3] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,2,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,1,2,2] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[2,2,1,1,1] => [2,3] => [1,1] => [1,0,1,0] => 2
[2,2,1,2] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[2,2,2,1] => [3,1] => [1,1] => [1,0,1,0] => 2
[2,2,3] => [2,1] => [1,1] => [1,0,1,0] => 2
[2,3,1,1] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[3,1,1,1,1] => [1,4] => [1,1] => [1,0,1,0] => 2
[3,1,1,2] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,2,1,1] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[3,2,2] => [1,2] => [1,1] => [1,0,1,0] => 2
[3,3,1] => [2,1] => [1,1] => [1,0,1,0] => 2
[4,1,1,1] => [1,3] => [1,1] => [1,0,1,0] => 2
[5,1,1] => [1,2] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,1,1,2] => [6,1] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,1,2,1] => [5,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,3] => [5,1] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,2,1,1] => [4,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,2,2] => [4,2] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,3,1] => [4,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,4] => [4,1] => [1,1] => [1,0,1,0] => 2
[1,1,1,2,1,1,1] => [3,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,2,1,2] => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,2,2,1] => [3,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,2,3] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,3,1,1] => [3,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,3,2] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,4,1] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,5] => [3,1] => [1,1] => [1,0,1,0] => 2
[1,1,2,1,1,1,1] => [2,1,4] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,2,1,1,2] => [2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,2,1,2,1] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,2,1,3] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,2,2,2] => [2,3] => [1,1] => [1,0,1,0] => 2
[1,1,2,3,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,2,4] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,3,1,1,1] => [2,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,3,1,2] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,3,2,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,4,1,1] => [2,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,4,2] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,5,1] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,6] => [2,1] => [1,1] => [1,0,1,0] => 2
[1,2,1,1,1,1,1] => [1,1,5] => [2,1] => [1,1,0,0,1,0] => 2
[1,2,1,1,1,2] => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,2,1,1,2,1] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,3] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,2,1,2,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,2,1,2,2] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,2,2,1,1,1] => [1,2,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,2,2,1,2] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,2,2,2,1] => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
>>> Load all 1717 entries. <<<[1,2,2,3] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,2,3,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,3,1,1,1,1] => [1,1,4] => [2,1] => [1,1,0,0,1,0] => 2
[1,3,1,1,2] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,3,2,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,3,2,2] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[1,3,3,1] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,4,1,1,1] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[1,5,1,1] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[2,1,1,1,1,1,1] => [1,6] => [1,1] => [1,0,1,0] => 2
[2,1,1,1,1,2] => [1,4,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,1,1,2,1] => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1,3] => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,1,2,1,1] => [1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,1,2,2] => [1,2,2] => [1,2] => [1,0,1,1,0,0] => 2
[2,1,1,3,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,4] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,2,1,1,1] => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,1,2,2,1] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,1,3,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,2,1,1,1,1] => [2,4] => [1,1] => [1,0,1,0] => 2
[2,2,1,1,2] => [2,2,1] => [2,1] => [1,1,0,0,1,0] => 2
[2,2,1,2,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[2,2,1,3] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[2,2,2,1,1] => [3,2] => [1,1] => [1,0,1,0] => 2
[2,2,3,1] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[2,2,4] => [2,1] => [1,1] => [1,0,1,0] => 2
[2,3,1,1,1] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[2,3,3] => [1,2] => [1,1] => [1,0,1,0] => 2
[2,4,1,1] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[3,1,1,1,1,1] => [1,5] => [1,1] => [1,0,1,0] => 2
[3,1,1,1,2] => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,1,1,2,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[3,1,1,3] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,1,2,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[3,1,2,2] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[3,2,1,1,1] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[3,2,2,1] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,3,2] => [2,1] => [1,1] => [1,0,1,0] => 2
[4,1,1,1,1] => [1,4] => [1,1] => [1,0,1,0] => 2
[4,1,1,2] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[4,2,1,1] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[4,2,2] => [1,2] => [1,1] => [1,0,1,0] => 2
[5,1,1,1] => [1,3] => [1,1] => [1,0,1,0] => 2
[6,1,1] => [1,2] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,1,1,1,2] => [7,1] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,1,1,2,1] => [6,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,1,3] => [6,1] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,1,2,1,1] => [5,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,1,2,2] => [5,2] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,1,3,1] => [5,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,4] => [5,1] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,2,1,1,1] => [4,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,2,1,2] => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,2,2,1] => [4,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,2,3] => [4,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,3,1,1] => [4,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,3,2] => [4,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,4,1] => [4,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,5] => [4,1] => [1,1] => [1,0,1,0] => 2
[1,1,1,2,1,1,1,1] => [3,1,4] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,2,1,1,2] => [3,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,2,1,2,1] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,2,1,3] => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,2,2,1,1] => [3,2,2] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,2,3,1] => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,2,4] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,3,1,1,1] => [3,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,3,1,2] => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,3,2,1] => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,3,3] => [3,2] => [1,1] => [1,0,1,0] => 2
[1,1,1,4,1,1] => [3,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,4,2] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,5,1] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,6] => [3,1] => [1,1] => [1,0,1,0] => 2
[1,1,2,1,1,1,1,1] => [2,1,5] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,2,1,1,1,2] => [2,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,2,1,1,2,1] => [2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,2,1,1,3] => [2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,2,1,2,1,1] => [2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,2,1,2,2] => [2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,2,1,3,1] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,2,1,4] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,2,2,1,1,1] => [2,2,3] => [2,1] => [1,1,0,0,1,0] => 2
[1,1,2,2,1,2] => [2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,1,2,2,2,1] => [2,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,2,2,3] => [2,2,1] => [2,1] => [1,1,0,0,1,0] => 2
[1,1,2,3,1,1] => [2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,2,3,2] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,2,4,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,2,5] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,3,1,1,1,1] => [2,1,4] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,3,1,1,2] => [2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,3,1,2,1] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,3,1,3] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,3,2,1,1] => [2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,3,2,2] => [2,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,3,3,1] => [2,2,1] => [2,1] => [1,1,0,0,1,0] => 2
[1,1,3,4] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,4,1,1,1] => [2,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,4,1,2] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,4,2,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,4,3] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,5,1,1] => [2,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,5,2] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,6,1] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,7] => [2,1] => [1,1] => [1,0,1,0] => 2
[1,2,1,1,1,1,1,1] => [1,1,6] => [2,1] => [1,1,0,0,1,0] => 2
[1,2,1,1,1,1,2] => [1,1,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,2,1,1,1,2,1] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,1,3] => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,2,1,1,2,1,1] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,2,1,1,2,2] => [1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,2,1,1,3,1] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,4] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,2,1,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,2,1,2,2,1] => [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,2,1,3,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,2,2,1,1,1,1] => [1,2,4] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,2,2,1,1,2] => [1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,2,2,1,2,1] => [1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,2,2,1,3] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,2,2,2,1,1] => [1,3,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,2,2,2,2] => [1,4] => [1,1] => [1,0,1,0] => 2
[1,2,2,3,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,2,2,4] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,2,3,1,1,1] => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,2,3,3] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[1,2,4,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,3,1,1,1,1,1] => [1,1,5] => [2,1] => [1,1,0,0,1,0] => 2
[1,3,1,1,1,2] => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,3,1,1,2,1] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,3,1,1,3] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,3,1,2,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,3,1,2,2] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,3,2,1,1,1] => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,3,2,2,1] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,3,3,1,1] => [1,2,2] => [1,2] => [1,0,1,1,0,0] => 2
[1,3,3,2] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,4,1,1,1,1] => [1,1,4] => [2,1] => [1,1,0,0,1,0] => 2
[1,4,1,1,2] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,4,2,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,4,2,2] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[1,4,4] => [1,2] => [1,1] => [1,0,1,0] => 2
[1,5,1,1,1] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[1,6,1,1] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[2,1,1,1,1,1,1,1] => [1,7] => [1,1] => [1,0,1,0] => 2
[2,1,1,1,1,1,2] => [1,5,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,1,1,1,2,1] => [1,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1,1,3] => [1,4,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,1,1,2,1,1] => [1,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,1,1,2,2] => [1,3,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,1,1,3,1] => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1,4] => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,1,2,1,1,1] => [1,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,1,2,1,2] => [1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,1,1,2,2,1] => [1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[2,1,1,2,3] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,3,1,1] => [1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,1,3,2] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,4,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,5] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,2,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,1,2,1,1,2] => [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[2,1,2,2,1,1] => [1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[2,1,2,2,2] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[2,1,3,1,1,1] => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,1,3,3] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[2,1,4,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,2,1,1,1,1,1] => [2,5] => [1,1] => [1,0,1,0] => 2
[2,2,1,1,1,2] => [2,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,2,1,1,2,1] => [2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[2,2,1,1,3] => [2,2,1] => [2,1] => [1,1,0,0,1,0] => 2
[2,2,1,2,1,1] => [2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[2,2,1,2,2] => [2,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,2,1,3,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[2,2,1,4] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[2,2,2,1,2] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[2,2,2,2,1] => [4,1] => [1,1] => [1,0,1,0] => 2
[2,2,2,3] => [3,1] => [1,1] => [1,0,1,0] => 2
[2,2,3,1,1] => [2,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,2,3,2] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[2,2,4,1] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[2,2,5] => [2,1] => [1,1] => [1,0,1,0] => 2
[2,3,1,1,1,1] => [1,1,4] => [2,1] => [1,1,0,0,1,0] => 2
[2,3,1,1,2] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,3,2,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,3,2,2] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[2,3,3,1] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,4,1,1,1] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[2,5,1,1] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[3,1,1,1,1,1,1] => [1,6] => [1,1] => [1,0,1,0] => 2
[3,1,1,1,1,2] => [1,4,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,1,1,1,2,1] => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[3,1,1,1,3] => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,1,1,2,1,1] => [1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[3,1,1,2,2] => [1,2,2] => [1,2] => [1,0,1,1,0,0] => 2
[3,1,1,3,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[3,1,1,4] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,1,2,1,1,1] => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[3,1,2,2,1] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[3,1,3,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[3,2,1,1,1,1] => [1,1,4] => [2,1] => [1,1,0,0,1,0] => 2
[3,2,1,1,2] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[3,2,2,1,1] => [1,2,2] => [1,2] => [1,0,1,1,0,0] => 2
[3,2,2,2] => [1,3] => [1,1] => [1,0,1,0] => 2
[3,3,1,1,1] => [2,3] => [1,1] => [1,0,1,0] => 2
[3,3,1,2] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[3,3,2,1] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[3,4,1,1] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[4,1,1,1,1,1] => [1,5] => [1,1] => [1,0,1,0] => 2
[4,1,1,1,2] => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[4,1,1,2,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[4,1,1,3] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[4,1,2,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[4,1,2,2] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[4,2,1,1,1] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[4,2,2,1] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[4,3,1,1] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[4,4,1] => [2,1] => [1,1] => [1,0,1,0] => 2
[5,1,1,1,1] => [1,4] => [1,1] => [1,0,1,0] => 2
[5,1,1,2] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[5,2,1,1] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[5,2,2] => [1,2] => [1,1] => [1,0,1,0] => 2
[6,1,1,1] => [1,3] => [1,1] => [1,0,1,0] => 2
[7,1,1] => [1,2] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,1,1,1,1,2] => [8,1] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,1,1,1,2,1] => [7,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,1,1,3] => [7,1] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,1,1,2,1,1] => [6,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,1,1,2,2] => [6,2] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,1,1,3,1] => [6,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,1,4] => [6,1] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,1,2,1,1,1] => [5,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,1,2,1,2] => [5,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,2,2,1] => [5,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,1,2,3] => [5,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,3,1,1] => [5,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,1,3,2] => [5,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,4,1] => [5,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,5] => [5,1] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,2,1,1,1,1] => [4,1,4] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,2,1,1,2] => [4,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,2,1,2,1] => [4,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,2,1,3] => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,2,2,1,1] => [4,2,2] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,2,2,2] => [4,3] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,2,3,1] => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,2,4] => [4,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,3,1,1,1] => [4,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,3,1,2] => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,3,2,1] => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,3,3] => [4,2] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,4,1,1] => [4,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,4,2] => [4,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,5,1] => [4,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,6] => [4,1] => [1,1] => [1,0,1,0] => 2
[1,1,1,2,1,1,1,1,1] => [3,1,5] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,2,1,1,1,2] => [3,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,2,1,1,2,1] => [3,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,2,1,1,3] => [3,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,2,1,2,1,1] => [3,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,2,1,2,2] => [3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,1,2,1,3,1] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,2,1,4] => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,2,2,1,1,1] => [3,2,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,2,2,1,2] => [3,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,1,1,2,2,2,1] => [3,3,1] => [2,1] => [1,1,0,0,1,0] => 2
[1,1,1,2,2,3] => [3,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,2,3,1,1] => [3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,1,2,3,2] => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,2,4,1] => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,2,5] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,3,1,1,1,1] => [3,1,4] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,3,1,1,2] => [3,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,3,1,2,1] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,3,1,3] => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,3,2,1,1] => [3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,1,3,2,2] => [3,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,3,3,1] => [3,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,3,4] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,4,1,1,1] => [3,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,4,1,2] => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,4,2,1] => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,4,3] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,5,1,1] => [3,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,5,2] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,6,1] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,7] => [3,1] => [1,1] => [1,0,1,0] => 2
[1,1,2,1,1,1,1,1,1] => [2,1,6] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,2,1,1,1,1,2] => [2,1,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,2,1,1,1,2,1] => [2,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,2,1,1,1,3] => [2,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,2,1,1,2,1,1] => [2,1,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[1,1,2,1,1,2,2] => [2,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,1,2,1,1,3,1] => [2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,2,1,1,4] => [2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,2,1,2,1,1,1] => [2,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,2,1,2,1,2] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,2,1,2,2,1] => [2,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[1,1,2,1,2,3] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,2,1,3,1,1] => [2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,2,1,3,2] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,2,1,4,1] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,2,1,5] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,2,2,1,1,1,1] => [2,2,4] => [2,1] => [1,1,0,0,1,0] => 2
[1,1,2,2,1,1,2] => [2,2,2,1] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,1,2,2,1,2,1] => [2,2,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[1,1,2,2,1,3] => [2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,1,2,2,2,1,1] => [2,3,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,2,2,2,2] => [2,4] => [1,1] => [1,0,1,0] => 2
[1,1,2,2,3,1] => [2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,1,2,2,4] => [2,2,1] => [2,1] => [1,1,0,0,1,0] => 2
[1,1,2,3,1,1,1] => [2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,2,3,1,2] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,2,3,2,1] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,2,3,3] => [2,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,2,4,1,1] => [2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,2,4,2] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,2,5,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,2,6] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,3,1,1,1,1,1] => [2,1,5] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,3,1,1,1,2] => [2,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,3,1,1,2,1] => [2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,3,1,1,3] => [2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,3,1,2,1,1] => [2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,3,1,2,2] => [2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,3,1,3,1] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,3,1,4] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,3,2,1,1,1] => [2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,3,2,1,2] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,3,2,2,1] => [2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,3,2,3] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,3,3,2] => [2,2,1] => [2,1] => [1,1,0,0,1,0] => 2
[1,1,3,4,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,3,5] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,4,1,1,1,1] => [2,1,4] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,4,1,1,2] => [2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,4,1,2,1] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,4,1,3] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,4,2,1,1] => [2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,4,2,2] => [2,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,4,3,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,5,1,1,1] => [2,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,5,1,2] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,5,2,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,5,3] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,6,1,1] => [2,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,6,2] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,7,1] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,8] => [2,1] => [1,1] => [1,0,1,0] => 2
[1,2,1,1,1,1,1,1,1] => [1,1,7] => [2,1] => [1,1,0,0,1,0] => 2
[1,2,1,1,1,1,1,2] => [1,1,5,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,2,1,1,1,1,2,1] => [1,1,4,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,1,1,3] => [1,1,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,2,1,1,1,2,1,1] => [1,1,3,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,2,1,1,1,2,2] => [1,1,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,2,1,1,1,3,1] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,1,4] => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,2,1,1,2,1,1,1] => [1,1,2,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,2,1,1,2,1,2] => [1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,2,1,1,2,2,1] => [1,1,2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,2,1,1,2,3] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,3,1,1] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,2,1,1,3,2] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,4,1] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,5] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,2,1,2,1,1,1,1] => [1,1,1,1,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,2,1,2,1,1,2] => [1,1,1,1,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,2,1,2,2,1,1] => [1,1,1,2,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,2,1,2,2,2] => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,2,1,3,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,2,1,3,3] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,2,1,4,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,2,2,1,1,1,1,1] => [1,2,5] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,2,2,1,1,1,2] => [1,2,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,2,2,1,1,2,1] => [1,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,2,2,1,1,3] => [1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,2,2,1,2,1,1] => [1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,2,2,1,2,2] => [1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,2,2,1,3,1] => [1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,2,2,1,4] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,2,2,2,1,1,1] => [1,3,3] => [1,2] => [1,0,1,1,0,0] => 2
[1,2,2,2,1,2] => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,2,2,2,2,1] => [1,4,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,2,2,2,3] => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,2,2,3,1,1] => [1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,2,2,3,2] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,2,2,4,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,2,2,5] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,2,3,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,2,3,1,1,2] => [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,2,3,2,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,2,3,2,2] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,2,3,3,1] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,2,4,1,1,1] => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,2,5,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,3,1,1,1,1,1,1] => [1,1,6] => [2,1] => [1,1,0,0,1,0] => 2
[1,3,1,1,1,1,2] => [1,1,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,3,1,1,1,2,1] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,3,1,1,1,3] => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,3,1,1,2,1,1] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,3,1,1,2,2] => [1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,3,1,1,3,1] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,3,1,1,4] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,3,1,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,3,1,2,2,1] => [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,3,1,3,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,3,2,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,3,2,1,1,2] => [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,3,2,2,1,1] => [1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,3,2,2,2] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[1,3,3,1,1,1] => [1,2,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,3,3,1,2] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,3,3,2,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,3,3,3] => [1,3] => [1,1] => [1,0,1,0] => 2
[1,3,4,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,4,1,1,1,1,1] => [1,1,5] => [2,1] => [1,1,0,0,1,0] => 2
[1,4,1,1,1,2] => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,4,1,1,2,1] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,4,1,1,3] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,4,1,2,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,4,1,2,2] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,4,2,1,1,1] => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,4,2,2,1] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,4,3,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,4,4,1] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,5,1,1,1,1] => [1,1,4] => [2,1] => [1,1,0,0,1,0] => 2
[1,5,1,1,2] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,5,2,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,5,2,2] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[1,6,1,1,1] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[1,7,1,1] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[2,1,1,1,1,1,1,1,1] => [1,8] => [1,1] => [1,0,1,0] => 2
[2,1,1,1,1,1,1,2] => [1,6,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,1,1,1,1,2,1] => [1,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1,1,1,3] => [1,5,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,1,1,1,2,1,1] => [1,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,1,1,1,2,2] => [1,4,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,1,1,1,3,1] => [1,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1,1,4] => [1,4,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,1,1,2,1,1,1] => [1,3,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,1,1,2,1,2] => [1,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,1,1,1,2,2,1] => [1,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,1,1,2,3] => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1,3,1,1] => [1,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,1,1,3,2] => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1,4,1] => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1,5] => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,1,2,1,1,1,1] => [1,2,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,1,2,1,1,2] => [1,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[2,1,1,2,1,2,1] => [1,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,1,1,2,1,3] => [1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,1,1,2,2,1,1] => [1,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[2,1,1,2,2,2] => [1,2,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,1,2,3,1] => [1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,1,1,2,4] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,3,1,1,1] => [1,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,1,3,1,2] => [1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,1,1,3,2,1] => [1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,1,1,3,3] => [1,2,2] => [1,2] => [1,0,1,1,0,0] => 2
[2,1,1,4,1,1] => [1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,1,4,2] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,5,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,6] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,2,1,1,1,1,1] => [1,1,1,5] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,1,2,1,1,1,2] => [1,1,1,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[2,1,2,1,1,2,1] => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[2,1,2,1,1,3] => [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[2,1,2,1,2,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[2,1,2,1,2,2] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[2,1,2,2,1,1,1] => [1,1,2,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,1,2,2,1,2] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[2,1,2,2,2,1] => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,1,2,2,3] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,1,2,3,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[2,1,3,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,1,3,1,1,2] => [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[2,1,3,2,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[2,1,3,2,2] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,1,3,3,1] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,1,4,1,1,1] => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,1,5,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,2,1,1,1,1,1,1] => [2,6] => [1,1] => [1,0,1,0] => 2
[2,2,1,1,1,1,2] => [2,4,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,2,1,1,1,2,1] => [2,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,2,1,1,1,3] => [2,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,2,1,1,2,1,1] => [2,2,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,2,1,1,3,1] => [2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[2,2,1,1,4] => [2,2,1] => [2,1] => [1,1,0,0,1,0] => 2
[2,2,1,2,1,1,1] => [2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[2,2,1,2,1,2] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[2,2,1,2,2,1] => [2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,2,1,2,3] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[2,2,1,3,1,1] => [2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[2,2,1,3,2] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[2,2,1,4,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[2,2,1,5] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[2,2,2,1,1,1,1] => [3,4] => [1,1] => [1,0,1,0] => 2
[2,2,2,1,1,2] => [3,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,2,2,1,2,1] => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[2,2,2,1,3] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[2,2,2,2,1,1] => [4,2] => [1,1] => [1,0,1,0] => 2
[2,2,2,3,1] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[2,2,2,4] => [3,1] => [1,1] => [1,0,1,0] => 2
[2,2,3,1,1,1] => [2,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,2,3,1,2] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[2,2,3,2,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[2,2,4,1,1] => [2,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,2,4,2] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[2,2,5,1] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[2,2,6] => [2,1] => [1,1] => [1,0,1,0] => 2
[2,3,1,1,1,1,1] => [1,1,5] => [2,1] => [1,1,0,0,1,0] => 2
[2,3,1,1,1,2] => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,3,1,1,2,1] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[2,3,1,1,3] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,3,1,2,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[2,3,1,2,2] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,3,2,1,1,1] => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,3,2,2,1] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,3,3,1,1] => [1,2,2] => [1,2] => [1,0,1,1,0,0] => 2
[2,3,3,2] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,4,1,1,1,1] => [1,1,4] => [2,1] => [1,1,0,0,1,0] => 2
[2,4,1,1,2] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,4,2,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,4,2,2] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[2,4,4] => [1,2] => [1,1] => [1,0,1,0] => 2
[2,5,1,1,1] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[2,6,1,1] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[3,1,1,1,1,1,1,1] => [1,7] => [1,1] => [1,0,1,0] => 2
[3,1,1,1,1,1,2] => [1,5,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,1,1,1,1,2,1] => [1,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[3,1,1,1,1,3] => [1,4,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,1,1,1,2,1,1] => [1,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[3,1,1,1,2,2] => [1,3,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,1,1,1,3,1] => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[3,1,1,1,4] => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,1,1,2,1,1,1] => [1,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[3,1,1,2,1,2] => [1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[3,1,1,2,2,1] => [1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[3,1,1,2,3] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[3,1,1,3,1,1] => [1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[3,1,1,3,2] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[3,1,1,4,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[3,1,1,5] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,1,2,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[3,1,2,1,1,2] => [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[3,1,2,2,1,1] => [1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[3,1,2,2,2] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[3,1,3,1,1,1] => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[3,1,3,3] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[3,1,4,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[3,2,1,1,1,1,1] => [1,1,5] => [2,1] => [1,1,0,0,1,0] => 2
[3,2,1,1,1,2] => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[3,2,1,1,2,1] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[3,2,1,1,3] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[3,2,1,2,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[3,2,1,2,2] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[3,2,2,1,1,1] => [1,2,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,2,2,1,2] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[3,2,2,2,1] => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,2,2,3] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,2,3,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[3,3,1,1,1,1] => [2,4] => [1,1] => [1,0,1,0] => 2
[3,3,1,1,2] => [2,2,1] => [2,1] => [1,1,0,0,1,0] => 2
[3,3,1,2,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[3,3,1,3] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[3,3,2,1,1] => [2,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,3,3,1] => [3,1] => [1,1] => [1,0,1,0] => 2
[3,3,4] => [2,1] => [1,1] => [1,0,1,0] => 2
[3,4,1,1,1] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[3,5,1,1] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[4,1,1,1,1,1,1] => [1,6] => [1,1] => [1,0,1,0] => 2
[4,1,1,1,1,2] => [1,4,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[4,1,1,1,2,1] => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[4,1,1,1,3] => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[4,1,1,2,1,1] => [1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[4,1,1,2,2] => [1,2,2] => [1,2] => [1,0,1,1,0,0] => 2
[4,1,1,3,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[4,1,1,4] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[4,1,2,1,1,1] => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[4,1,2,2,1] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[4,1,3,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[4,2,1,1,1,1] => [1,1,4] => [2,1] => [1,1,0,0,1,0] => 2
[4,2,1,1,2] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[4,2,2,1,1] => [1,2,2] => [1,2] => [1,0,1,1,0,0] => 2
[4,2,2,2] => [1,3] => [1,1] => [1,0,1,0] => 2
[4,3,1,1,1] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[4,3,3] => [1,2] => [1,1] => [1,0,1,0] => 2
[4,4,2] => [2,1] => [1,1] => [1,0,1,0] => 2
[5,1,1,1,1,1] => [1,5] => [1,1] => [1,0,1,0] => 2
[5,1,1,1,2] => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[5,1,1,2,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[5,1,1,3] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[5,1,2,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[5,1,2,2] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[5,2,1,1,1] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[5,2,2,1] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[5,3,1,1] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[6,1,1,1,1] => [1,4] => [1,1] => [1,0,1,0] => 2
[6,1,1,2] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[6,2,1,1] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[6,2,2] => [1,2] => [1,1] => [1,0,1,0] => 2
[7,1,1,1] => [1,3] => [1,1] => [1,0,1,0] => 2
[8,1,1] => [1,2] => [1,1] => [1,0,1,0] => 2
[1,8,1,1] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[1,1,8,1] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,1,1,1,2,2] => [8,2] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,1,1,2,2,1,1] => [6,2,2] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,1,2,1,1,2] => [6,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,3,3] => [6,2] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,2,2,1,1,1,1] => [4,2,4] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,2,1,1,2,1,1] => [4,1,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,2,1,1,1,1,2] => [4,1,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,2,1,2,3] => [4,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,3,3,1,1] => [4,2,2] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,3,2,1,2] => [4,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,3,1,1,3] => [4,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,4,4] => [4,2] => [1,1] => [1,0,1,0] => 2
[1,1,2,2,1,1,1,1,1,1] => [2,2,6] => [2,1] => [1,1,0,0,1,0] => 2
[1,1,2,2,2,2,1,1] => [2,4,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,2,2,2,1,1,2] => [2,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,2,1,1,2,1,1,1,1] => [2,1,2,1,4] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[1,1,2,1,1,2,2,2] => [2,1,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,2,1,1,1,1,2,1,1] => [2,1,4,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[1,1,2,1,1,1,1,1,1,2] => [2,1,6,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,2,1,1,1,2,3] => [2,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,2,1,2,3,1,1] => [2,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,2,1,2,2,1,2] => [2,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,2,1,2,1,1,3] => [2,1,1,1,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,2,1,3,4] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,3,3,1,1,1,1] => [2,2,4] => [2,1] => [1,1,0,0,1,0] => 2
[1,1,3,2,1,2,1,1] => [2,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,3,2,1,1,1,2] => [2,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[1,1,3,2,2,3] => [2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,3,1,1,3,1,1] => [2,1,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[1,1,3,1,1,2,1,2] => [2,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,3,1,1,1,1,3] => [2,1,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,3,1,2,4] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,4,3,1,2] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,4,2,1,3] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,4,1,1,4] => [2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,2,1,1,1,1,1,1,1,1] => [2,8] => [1,1] => [1,0,1,0] => 2
[2,2,1,1,1,1,2,2] => [2,4,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,2,1,1,2,1,1,2] => [2,2,1,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[2,2,2,1,1,2,1,1] => [3,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,2,2,1,1,1,1,2] => [3,4,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,2,2,1,2,3] => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[2,2,3,2,1,2] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[2,2,3,1,1,3] => [2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,1,2,1,1,1,1,1,1] => [1,2,1,6] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,1,2,1,1,2,2] => [1,2,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[2,1,1,2,2,2,1,1] => [1,2,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,1,2,2,1,1,2] => [1,2,2,2,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[2,1,1,2,3,3] => [1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,1,1,1,2,1,1,1,1] => [1,4,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,1,1,1,2,2,2] => [1,4,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,1,1,1,1,1,2,1,1] => [1,6,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,1,1,1,1,1,1,1,2] => [1,8,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,1,1,1,1,2,3] => [1,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1,2,3,1,1] => [1,3,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[2,1,1,1,2,2,1,2] => [1,3,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[2,1,1,1,2,1,1,3] => [1,3,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[2,1,1,1,3,4] => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,2,3,1,1,1,1] => [1,1,1,1,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[2,1,2,3,2,2] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[2,1,2,2,1,2,1,1] => [1,1,2,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[2,1,2,2,1,1,1,2] => [1,1,2,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[2,1,2,2,2,3] => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,1,2,1,1,3,1,1] => [1,1,1,2,1,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 2
[2,1,2,1,1,1,1,3] => [1,1,1,4,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[2,1,3,4,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[2,1,3,3,1,2] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[2,1,3,1,1,4] => [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[3,3,1,1,1,1,1,1] => [2,6] => [1,1] => [1,0,1,0] => 2
[3,3,2,1,1,2] => [2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[3,2,1,2,1,1,1,1] => [1,1,1,1,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[3,2,1,2,2,2] => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[3,2,1,1,1,2,1,1] => [1,1,3,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[3,2,1,1,1,1,1,2] => [1,1,5,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[3,2,1,1,2,3] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[3,2,2,3,1,1] => [1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[3,2,2,2,1,2] => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[3,2,2,1,1,3] => [1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[3,1,1,3,1,1,1,1] => [1,2,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[3,1,1,3,2,2] => [1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[3,1,1,2,1,2,1,1] => [1,2,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
[3,1,1,2,1,1,1,2] => [1,2,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[3,1,1,2,2,3] => [1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[3,1,1,1,1,3,1,1] => [1,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[3,1,1,1,1,2,1,2] => [1,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[3,1,1,1,1,1,1,3] => [1,6,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,1,1,1,2,4] => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[3,1,2,4,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[3,1,2,2,1,3] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[3,1,2,1,1,4] => [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[4,4,1,1,1,1] => [2,4] => [1,1] => [1,0,1,0] => 2
[4,3,1,2,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[4,3,1,1,1,2] => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[4,2,1,3,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[4,2,1,1,1,3] => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[4,2,2,4] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[4,1,1,4,1,1] => [1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[4,1,1,3,1,2] => [1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[4,1,1,2,1,3] => [1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[4,1,1,1,1,4] => [1,4,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[5,1,1,5] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,2,2,2,2,2,1] => [1,5,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,2,2,2,3,2] => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,2,2,3,3,1] => [1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,2,2,3,2,2] => [1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,2,2,4,3] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,2,3,3,2,1] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,3,2,2,2] => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,2,3,3,3] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[1,2,4,4,1] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,3,3,2,2,1] => [1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,3,3,3,2] => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,3,4,2,2] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,3,2,2,3,1] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,3,2,2,2,2] => [1,1,4] => [2,1] => [1,1,0,0,1,0] => 2
[1,3,2,3,3] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,3,3,4,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,3,3,2,3] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,3,4,4] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[1,4,4,2,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,4,3,3,1] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,4,3,2,2] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,4,4,3] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,4,2,2,3] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,5,5,1] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,5,3,3] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[2,3,2,2,2,1] => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,3,3,3,1] => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,3,3,2,2] => [1,2,2] => [1,2] => [1,0,1,1,0,0] => 2
[2,4,4,2] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,4,2,2,2] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[2,4,3,3] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[2,2,3,2,2,1] => [2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,2,3,3,2] => [2,2,1] => [2,1] => [1,1,0,0,1,0] => 2
[2,2,4,3,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[2,2,4,2,2] => [2,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,2,5,3] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[2,2,2,3,2,1] => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[2,2,2,4,2] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[2,2,2,2,3,1] => [4,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[2,2,2,3,3] => [3,2] => [1,1] => [1,0,1,0] => 2
[2,2,3,4,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[2,2,3,2,3] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[2,3,2,2,3] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,3,3,4] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,5,5] => [1,2] => [1,1] => [1,0,1,0] => 2
[3,4,2,2,1] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[3,5,2,2] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[3,3,3,2,1] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[3,3,4,2] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[3,3,2,3,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[3,3,2,2,2] => [2,3] => [1,1] => [1,0,1,0] => 2
[3,4,4,1] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,2,3,3,1] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[3,2,3,2,2] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[3,2,2,4,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[3,2,2,3,2] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[3,2,2,2,3] => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,3,5,1] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[3,3,2,4] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[4,4,3,1] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[4,3,3,2] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[4,2,3,3] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[5,5,2] => [2,1] => [1,1] => [1,0,1,0] => 2
[1,6,1,1,2] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,5,1,1,1,2] => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,4,1,1,1,1,2] => [1,1,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,3,1,1,1,1,1,2] => [1,1,5,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,2,1,1,1,1,1,1,2] => [1,1,6,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,1,1,2] => [9,1] => [1,1] => [1,0,1,0] => 2
[1,6,2,2] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[1,7,1,1,2] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,6,1,1,1,2] => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,4,2,1,1,2] => [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,5,1,1,1,1,2] => [1,1,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,3,2,1,1,1,2] => [1,1,1,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,4,1,1,1,1,1,2] => [1,1,5,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,2,2,1,1,1,1,2] => [1,2,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,3,1,1,1,1,1,1,2] => [1,1,6,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,1,2,1,1,1,1,1,2] => [2,1,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,2,1,1,1,1,1,1,1,2] => [1,1,7,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,1,1,1,2] => [10,1] => [1,1] => [1,0,1,0] => 2
[1,2,2,2,2,2] => [1,5] => [1,1] => [1,0,1,0] => 2
[1,2,2,2,1,3] => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,2,2,1,3,2] => [1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,2,2,1,2,3] => [1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,2,2,1,1,4] => [1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,2,1,3,2,2] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,2,1,2,2,3] => [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,2,1,1,4,2] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,3,3] => [1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,2,1,1,2,4] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,1,5] => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,1,3,2,2,2] => [2,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,3,2,1,3] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,3,1,3,2] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,3,1,2,3] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,3,1,1,4] => [2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,2,3,2,2] => [2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,2,3,1,3] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,2,2,3,2] => [2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,1,2,2,2,3] => [2,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,2,2,1,4] => [2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,1,2,1,4,2] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,2,1,3,3] => [2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,2,1,2,4] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,2,1,1,5] => [2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,4,2,2] => [3,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,4,1,3] => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,3,3,2] => [3,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,3,2,3] => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,3,1,4] => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,2,4,2] => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,2,3,3] => [3,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,2,2,4] => [3,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,2,1,5] => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,5,2] => [4,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,4,3] => [4,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,3,4] => [4,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,2,5] => [4,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,6] => [5,1] => [1,1] => [1,0,1,0] => 2
[1,2,2,2,2,2,2] => [1,6] => [1,1] => [1,0,1,0] => 2
[1,2,2,2,2,1,3] => [1,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,2,2,2,1,3,2] => [1,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,2,2,2,1,2,3] => [1,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,2,2,2,1,1,4] => [1,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,2,2,1,3,2,2] => [1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,2,2,1,3,1,3] => [1,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,2,2,1,2,3,2] => [1,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,2,2,1,2,2,3] => [1,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[1,2,2,1,2,1,4] => [1,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,2,2,1,1,4,2] => [1,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,2,2,1,1,3,3] => [1,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,2,2,1,1,2,4] => [1,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,2,2,1,1,1,5] => [1,2,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,2,1,3,2,2,2] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,2,1,3,1,1,4] => [1,1,1,1,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,2,1,2,3,2,2] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,2,1,2,2,3,2] => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,2,1,2,2,2,3] => [1,1,1,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,2,1,2,2,1,4] => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,2,1,2,1,3,3] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,2,1,2,1,1,5] => [1,1,1,1,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,2,1,1,4,2,2] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,2,1,1,4,1,3] => [1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,2,1,1,3,3,2] => [1,1,2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,2,1,1,3,2,3] => [1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,2,1,1,3,1,4] => [1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,2,1,1,2,4,2] => [1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,2,1,1,2,3,3] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,2,1,1,2,2,4] => [1,1,2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,2,1,1,2,1,5] => [1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,2,1,1,1,5,2] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,1,4,3] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,1,3,4] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,1,2,5] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,1,1,6] => [1,1,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,1,3,2,2,2,2] => [2,1,4] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,3,2,2,1,3] => [2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,3,2,1,3,2] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,3,2,1,2,3] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,3,2,1,1,4] => [2,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[1,1,3,1,3,2,2] => [2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,3,1,3,1,3] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,3,1,2,3,2] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,3,1,2,2,3] => [2,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[1,1,3,1,2,1,4] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,3,1,1,4,2] => [2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,3,1,1,3,3] => [2,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,1,3,1,1,2,4] => [2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,3,1,1,1,5] => [2,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,2,3,2,2,2] => [2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,2,3,2,1,3] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,2,3,1,3,2] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,2,3,1,2,3] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,2,3,1,1,4] => [2,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[1,1,2,2,3,2,2] => [2,2,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,1,2,2,3,1,3] => [2,2,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[1,1,2,2,2,3,2] => [2,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,1,2,2,2,2,3] => [2,4,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,2,2,2,1,4] => [2,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,1,2,2,1,4,2] => [2,2,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[1,1,2,2,1,3,3] => [2,2,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,1,2,2,1,2,4] => [2,2,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[1,1,2,2,1,1,5] => [2,2,2,1] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,1,2,1,4,2,2] => [2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,2,1,4,1,3] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,2,1,3,3,2] => [2,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[1,1,2,1,3,2,3] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,2,1,3,1,4] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,2,1,2,4,2] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,2,1,2,3,3] => [2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,2,1,2,2,4] => [2,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[1,1,2,1,2,1,5] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,2,1,1,5,2] => [2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,2,1,1,4,3] => [2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,2,1,1,3,4] => [2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,2,1,1,2,5] => [2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,2,1,1,1,6] => [2,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,4,2,2,2] => [3,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,4,2,1,3] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,4,1,3,2] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,4,1,2,3] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,4,1,1,4] => [3,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,3,3,2,2] => [3,2,2] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,3,3,1,3] => [3,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,1,1,3,2,3,2] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,3,2,2,3] => [3,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,3,2,1,4] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,3,1,4,2] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,3,1,3,3] => [3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,1,3,1,2,4] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,3,1,1,5] => [3,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,2,4,2,2] => [3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,1,2,4,1,3] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,2,3,3,2] => [3,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,2,3,2,3] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,2,3,1,4] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,2,2,4,2] => [3,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,1,1,2,2,3,3] => [3,2,2] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,2,2,2,4] => [3,3,1] => [2,1] => [1,1,0,0,1,0] => 2
[1,1,1,2,2,1,5] => [3,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,1,1,2,1,5,2] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,2,1,4,3] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,2,1,3,4] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,2,1,2,5] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,2,1,1,6] => [3,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,5,2,2] => [4,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,5,1,3] => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,4,3,2] => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,4,2,3] => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,4,1,4] => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,3,4,2] => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,3,3,3] => [4,3] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,3,2,4] => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,3,1,5] => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,2,5,2] => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,2,4,3] => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,2,3,4] => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,2,2,5] => [4,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,2,1,6] => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,6,2] => [5,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,5,3] => [5,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,4,4] => [5,2] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,1,3,5] => [5,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,2,6] => [5,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,1,7] => [6,1] => [1,1] => [1,0,1,0] => 2
[1,1,2,1,7] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,2,2,2,5] => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,2,3,5] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,4,1,5] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,2,1,1,5] => [3,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,2,1,2,2,3] => [2,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[1,1,2,5,3] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[3,1,2,3,3] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,1,4,3,3] => [2,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,2,1,3,3] => [3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,2,2,1,2,1,3] => [1,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[3,3,2,1,3] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,2,2,2,1,3] => [2,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,1,6,1,3] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,2,3,1,3] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[3,1,1,2,1,1,3] => [1,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[1,3,1,2,1,1,3] => [1,1,1,1,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,3,2,1,1,3] => [2,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,4,1,1,3] => [3,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,2,1,1,1,3] => [4,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,2,1,4,2,1] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[5,2,2,2,1] => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,6,2,2,1] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,1,2,3,2,2,1] => [2,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[3,1,2,1,2,2,1] => [1,1,1,1,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,3,2,1,2,2,1] => [1,1,1,1,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,4,1,2,2,1] => [2,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,2,1,1,2,2,1] => [3,1,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,1,2,1,2,4,1] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,2,2,6,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,1,2,7,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,4,5,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,2,1,5,1] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,2,2,1,2,3,1] => [1,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,2,2,2,3,1] => [2,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,1,6,3,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,2,3,3,1] => [3,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[3,1,1,2,1,3,1] => [1,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,3,2,1,3,1] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,4,1,3,1] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,2,1,1,3,1] => [4,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[7,1,2,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,2,4,1,2,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[3,2,2,1,2,1,1] => [1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,4,2,1,2,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,3,2,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,2,2,3,2,1,1] => [1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[3,5,2,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,7,2,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,1,2,4,2,1,1] => [2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[3,1,2,2,2,1,1] => [1,1,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,3,2,2,2,1,1] => [1,1,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,1,4,2,2,1,1] => [2,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,1,1,2,1,2,2,1,1] => [3,1,1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[5,1,4,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,2,2,1,4,1,1] => [1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[3,3,4,1,1] => [2,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,5,4,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,1,2,2,4,1,1] => [2,2,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[3,1,6,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,3,6,1,1] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,1,8,1,1] => [2,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,2,5,1,1] => [3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[3,1,1,2,3,1,1] => [1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,3,1,2,3,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,3,2,3,1,1] => [2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,4,3,1,1] => [3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,1,1,2,1,3,1,1] => [4,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[5,1,1,2,1,1,1] => [1,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,2,2,1,1,2,1,1,1] => [1,2,2,1,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[3,3,1,2,1,1,1] => [2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,5,1,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,1,2,2,1,2,1,1,1] => [2,2,1,1,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[3,1,3,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,3,3,2,1,1,1] => [1,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,5,2,1,1,1] => [2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[3,1,1,4,1,1,1] => [1,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,3,1,4,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,1,3,4,1,1,1] => [2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,1,6,1,1,1] => [3,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,2,3,1,1,1] => [4,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[3,1,1,1,2,1,1,1,1] => [1,3,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,3,1,1,2,1,1,1,1] => [1,1,2,1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,1,3,1,2,1,1,1,1] => [2,1,1,1,4] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,3,2,1,1,1,1] => [3,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,1,1,4,1,1,1,1] => [4,1,4] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,2,2,2,1,2,1] => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[2,2,2,1,2,1,2] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[2,2,2,1,2,2,1] => [3,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,2,2,1,1,2,2] => [3,2,2] => [1,2] => [1,0,1,1,0,0] => 2
[2,2,1,2,1,2,2] => [2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[2,2,1,2,1,1,2,1] => [2,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[2,2,1,2,2,1,2] => [2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[2,2,1,2,2,2,1] => [2,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,2,1,1,2,2,2] => [2,2,3] => [2,1] => [1,1,0,0,1,0] => 2
[2,2,1,1,2,1,2,1] => [2,2,1,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[2,2,1,1,1,2,2,1] => [2,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,2,1,2,2,2] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[2,1,2,1,1,2,2,1] => [1,1,1,2,2,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[2,1,2,1,1,1,2,2] => [1,1,1,3,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[2,1,2,2,1,2,2] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[2,1,2,2,1,1,2,1] => [1,1,2,2,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[2,1,2,2,2,1,2] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[2,1,2,2,2,2,1] => [1,1,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,1,1,2,2,2,2] => [1,2,4] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,1,2,2,1,2,1] => [1,2,2,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[2,1,1,2,1,2,2,1] => [1,2,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[2,1,1,1,2,2,2,1] => [1,3,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[2,1,1,1,2,1,2,2] => [1,3,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,2,1,2,2,2,2] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,2,1,2,1,1,2,2] => [1,1,1,1,2,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,2,1,1,2,1,2,2] => [1,1,2,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,2,1,1,2,2,1,2] => [1,1,2,2,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,2,1,1,2,2,2,1] => [1,1,2,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,2,1,1,1,2,2,2] => [1,1,3,3] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,2,1,1,1,1,2,2,1] => [1,1,4,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,2,2,1,2,2,2] => [1,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,2,2,1,1,2,1,2] => [1,2,2,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,2,2,1,1,2,2,1] => [1,2,2,2,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,2,2,1,1,1,2,2] => [1,2,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,2,2,2,1,2,2] => [1,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,2,2,2,1,1,2,1] => [1,3,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,2,2,2,2,1,2] => [1,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,1,2,2,2,2,2] => [2,5] => [1,1] => [1,0,1,0] => 2
[1,1,2,2,2,1,2,1] => [2,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,2,2,1,2,1,2] => [2,2,1,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,2,2,1,2,2,1] => [2,2,1,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,1,2,1,2,1,2,2] => [2,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,2,1,2,2,2,1] => [2,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[1,1,2,1,1,1,2,2,1] => [2,1,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,2,2,1,2,2] => [3,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,2,2,1,1,2,1] => [3,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,2,2,2,1,2] => [3,3,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,1,1,2,2,2,2,1] => [3,4,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,2,1,2,2,2] => [3,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,1,1,2,2,1,2,1] => [4,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,2,1,2,2,1] => [4,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,2,2,2,1] => [5,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,3,3,2] => [3,1] => [1,1] => [1,0,1,0] => 2
[3,4,4] => [1,2] => [1,1] => [1,0,1,0] => 2
[2,3,3,3] => [1,3] => [1,1] => [1,0,1,0] => 2
[4,4,3] => [2,1] => [1,1] => [1,0,1,0] => 2
[2,1,1,1,1,1,1,1,1,1] => [1,9] => [1,1] => [1,0,1,0] => 2
[3,2,2,2,2,1] => [1,4,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[4,3,2,2,1] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[4,2,2,3,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[4,2,2,2,2] => [1,4] => [1,1] => [1,0,1,0] => 2
[5,3,3,1] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[5,3,2,2] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[5,2,2,3] => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[6,3,3] => [1,2] => [1,1] => [1,0,1,0] => 2
[2,1,1,6,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1,5,1] => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1,1,4,1] => [1,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1,1,1,3,1] => [1,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1,1,1,1,2,1] => [1,6,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,2,6,1] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[2,1,1,7,1] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1,6,1] => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,2,4,1] => [1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,1,1,1,1,5,1] => [1,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1,2,3,1] => [1,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,1,1,1,1,1,4,1] => [1,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1,1,2,2,1] => [1,4,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,1,1,1,1,1,3,1] => [1,6,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1,1,1,2,1,1] => [1,5,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,1,1,1,1,1,1,2,1] => [1,7,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1,1,1,1,1,1,1,1] => [1,10] => [1,1] => [1,0,1,0] => 2
[2,2,2,2,2,1] => [5,1] => [1,1] => [1,0,1,0] => 2
[3,1,2,2,2,1] => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,3,1,2,2,1] => [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[3,2,1,2,2,1] => [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[4,1,1,2,2,1] => [1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[2,2,3,1,2,1] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[3,2,2,1,2,1] => [1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,4,1,1,2,1] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[3,3,1,1,2,1] => [2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[4,2,1,1,2,1] => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[5,1,1,1,2,1] => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,2,2,3,1,1] => [3,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,1,2,3,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[2,3,1,3,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[3,2,1,3,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[4,1,1,3,1,1] => [1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,2,3,2,1,1] => [2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[3,1,3,2,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[2,3,2,2,1,1] => [1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[3,2,2,2,1,1] => [1,3,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[4,1,2,2,1,1] => [1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[2,4,1,2,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[3,3,1,2,1,1] => [2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[4,2,1,2,1,1] => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[5,1,1,2,1,1] => [1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,2,4,1,1,1] => [2,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,1,4,1,1,1] => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,3,3,1,1,1] => [1,2,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,2,3,1,1,1] => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[4,1,3,1,1,1] => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,4,2,1,1,1] => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[3,3,2,1,1,1] => [2,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[4,2,2,1,1,1] => [1,2,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[5,1,2,1,1,1] => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,5,1,1,1,1] => [1,1,4] => [2,1] => [1,1,0,0,1,0] => 2
[3,4,1,1,1,1] => [1,1,4] => [2,1] => [1,1,0,0,1,0] => 2
[4,3,1,1,1,1] => [1,1,4] => [2,1] => [1,1,0,0,1,0] => 2
[5,2,1,1,1,1] => [1,1,4] => [2,1] => [1,1,0,0,1,0] => 2
[6,1,1,1,1,1] => [1,5] => [1,1] => [1,0,1,0] => 2
[2,2,2,2,2,2,1] => [6,1] => [1,1] => [1,0,1,0] => 2
[3,1,2,2,2,2,1] => [1,1,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,3,1,2,2,2,1] => [1,1,1,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[3,2,1,2,2,2,1] => [1,1,1,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[4,1,1,2,2,2,1] => [1,2,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,2,3,1,2,2,1] => [2,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[3,1,3,1,2,2,1] => [1,1,1,1,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[2,3,2,1,2,2,1] => [1,1,1,1,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[3,2,2,1,2,2,1] => [1,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[4,1,2,1,2,2,1] => [1,1,1,1,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[2,4,1,1,2,2,1] => [1,1,2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[3,3,1,1,2,2,1] => [2,2,2,1] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[4,2,1,1,2,2,1] => [1,1,2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[5,1,1,1,2,2,1] => [1,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,2,2,3,1,2,1] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[4,1,1,3,1,2,1] => [1,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,2,3,2,1,2,1] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,3,2,2,1,2,1] => [1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[3,2,2,2,1,2,1] => [1,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[4,1,2,2,1,2,1] => [1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[3,3,1,2,1,2,1] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[5,1,1,2,1,2,1] => [1,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,2,4,1,1,2,1] => [2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[3,1,4,1,1,2,1] => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[2,3,3,1,1,2,1] => [1,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[3,2,3,1,1,2,1] => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[4,1,3,1,1,2,1] => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[2,4,2,1,1,2,1] => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[3,3,2,1,1,2,1] => [2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[4,2,2,1,1,2,1] => [1,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[5,1,2,1,1,2,1] => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[2,5,1,1,1,2,1] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[3,4,1,1,1,2,1] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[4,3,1,1,1,2,1] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[5,2,1,1,1,2,1] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[6,1,1,1,1,2,1] => [1,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,2,2,2,3,1,1] => [4,1,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,1,2,2,3,1,1] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[2,3,1,2,3,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[3,2,1,2,3,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[4,1,1,2,3,1,1] => [1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[2,2,3,1,3,1,1] => [2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[3,1,3,1,3,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[2,3,2,1,3,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[3,2,2,1,3,1,1] => [1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[4,1,2,1,3,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[2,4,1,1,3,1,1] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[3,3,1,1,3,1,1] => [2,2,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[4,2,1,1,3,1,1] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[5,1,1,1,3,1,1] => [1,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,2,2,3,2,1,1] => [3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[3,1,2,3,2,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[2,3,1,3,2,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[3,2,1,3,2,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[4,1,1,3,2,1,1] => [1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[2,2,3,2,2,1,1] => [2,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[3,1,3,2,2,1,1] => [1,1,1,2,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[2,3,2,2,2,1,1] => [1,1,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[3,2,2,2,2,1,1] => [1,4,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[4,1,2,2,2,1,1] => [1,1,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,4,1,2,2,1,1] => [1,1,1,2,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[3,3,1,2,2,1,1] => [2,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[4,2,1,2,2,1,1] => [1,1,1,2,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[5,1,1,2,2,1,1] => [1,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[2,2,4,1,2,1,1] => [2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[3,1,4,1,2,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[2,3,3,1,2,1,1] => [1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[3,2,3,1,2,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[4,1,3,1,2,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[2,4,2,1,2,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[3,3,2,1,2,1,1] => [2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[4,2,2,1,2,1,1] => [1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[5,1,2,1,2,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[2,5,1,1,2,1,1] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[3,4,1,1,2,1,1] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[4,3,1,1,2,1,1] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[5,2,1,1,2,1,1] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[6,1,1,1,2,1,1] => [1,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,2,2,4,1,1,1] => [3,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,1,2,4,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[2,3,1,4,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[3,2,1,4,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[4,1,1,4,1,1,1] => [1,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,2,3,3,1,1,1] => [2,2,3] => [2,1] => [1,1,0,0,1,0] => 2
[3,1,3,3,1,1,1] => [1,1,2,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,3,2,3,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[3,2,2,3,1,1,1] => [1,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[4,1,2,3,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[2,4,1,3,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[3,3,1,3,1,1,1] => [2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[4,2,1,3,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[5,1,1,3,1,1,1] => [1,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,2,4,2,1,1,1] => [2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[3,1,4,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[2,3,3,2,1,1,1] => [1,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[3,2,3,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[4,1,3,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[2,4,2,2,1,1,1] => [1,1,2,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[3,3,2,2,1,1,1] => [2,2,3] => [2,1] => [1,1,0,0,1,0] => 2
[4,2,2,2,1,1,1] => [1,3,3] => [1,2] => [1,0,1,1,0,0] => 2
[5,1,2,2,1,1,1] => [1,1,2,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,5,1,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[3,4,1,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[4,3,1,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[5,2,1,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[6,1,1,2,1,1,1] => [1,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,2,5,1,1,1,1] => [2,1,4] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,1,5,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,3,4,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[3,2,4,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[4,1,4,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,4,3,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[3,3,3,1,1,1,1] => [3,4] => [1,1] => [1,0,1,0] => 2
[4,2,3,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[5,1,3,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,5,2,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[3,4,2,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[4,3,2,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[5,2,2,1,1,1,1] => [1,2,4] => [1,1,1] => [1,0,1,0,1,0] => 2
[6,1,2,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,6,1,1,1,1,1] => [1,1,5] => [2,1] => [1,1,0,0,1,0] => 2
[3,5,1,1,1,1,1] => [1,1,5] => [2,1] => [1,1,0,0,1,0] => 2
[4,4,1,1,1,1,1] => [2,5] => [1,1] => [1,0,1,0] => 2
[5,3,1,1,1,1,1] => [1,1,5] => [2,1] => [1,1,0,0,1,0] => 2
[6,2,1,1,1,1,1] => [1,1,5] => [2,1] => [1,1,0,0,1,0] => 2
[7,1,1,1,1,1,1] => [1,6] => [1,1] => [1,0,1,0] => 2
[2,2,1,2,1,2,1,1] => [2,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[2,2,1,1,1,2,1,1,1] => [2,3,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,2,1,1,1,2,1,1] => [1,1,1,3,1,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 2
[2,1,2,1,2,2,1,1] => [1,1,1,1,2,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[2,1,2,1,1,2,1,1,1] => [1,1,1,2,1,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 2
[2,1,1,2,1,1,1,2,1] => [1,2,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 2
[2,1,1,2,1,1,2,1,1] => [1,2,1,2,1,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 2
[2,1,1,2,1,2,1,1,1] => [1,2,1,1,1,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
[2,1,1,1,2,1,1,1,2] => [1,3,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[2,1,1,1,2,1,1,2,1] => [1,3,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 2
[2,1,1,1,2,1,2,1,1] => [1,3,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
[2,1,1,1,2,2,1,1,1] => [1,3,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,2,1,1,1,2,1,1,2] => [1,1,3,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,2,1,1,1,2,2,1,1] => [1,1,3,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,1,1,2,1,1,1] => [1,1,4,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,2,2,1,1,1,2,1,1] => [1,2,3,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[1,2,2,2,1,2,1,1] => [1,3,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,2,2,1,2,1,1,2] => [1,2,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,2,2,1,2,2,1,1] => [1,2,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,2,1,2,2,1,1,2] => [1,1,1,2,2,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,2,1,2,2,2,1,1] => [1,1,1,3,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,2,1,1,2,1,1,1,2] => [1,1,2,1,3,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,2,1,1,2,2,1,1,1] => [1,1,2,2,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,2,1,1,1,2,1,1,1,1] => [1,1,3,1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,1,2,1,1,1,2,1,2] => [2,1,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,2,1,1,2,1,1,2] => [2,1,2,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,2,1,1,2,2,1,1] => [2,1,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,2,1,1,1,2,1,1,1] => [2,1,3,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[1,1,2,2,1,1,1,2,1] => [2,2,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,1,2,2,1,1,2,1,1] => [2,2,2,1,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,1,2,1,2,1,1,1,2] => [2,1,1,1,3,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,2,1,2,2,1,1,1] => [2,1,1,2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,2,1,1,1,2,2] => [3,1,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,2,1,1,1,1,2,1] => [3,1,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,2,1,1,2,1,2] => [3,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,2,1,1,1,2,1,1] => [3,1,3,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,2,1,2,1,1,2] => [3,1,1,1,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,2,1,1,2,1,1,1] => [3,1,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,2,2,1,1,1,2] => [3,2,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,2,2,1,2,1,1] => [3,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,2,1,2,1,1,1,1] => [3,1,1,1,4] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,2,1,1,1,2,1] => [4,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,2,1,2,1,1,1] => [4,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[2,1,1,1,1,1,1,3] => [1,6,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,1,1,1,1,2,2] => [1,5,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,1,1,1,1,2,1,2] => [1,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,1,1,1,2,1,1,2] => [1,3,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[2,1,1,2,1,1,1,2] => [1,2,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[2,1,2,1,1,1,1,2] => [1,1,1,4,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[2,2,1,1,1,1,1,2] => [2,5,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,1,1,1,1,1,1,2] => [1,6,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,2,2,4,2,1] => [1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,2,4,2,2,1] => [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,2,5,2,2] => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,4,2,2,2,1] => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,5,2,2,2] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[2,5,2,2,1] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,6,2,2] => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 2
[2,2,5,2,1] => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[6,2,2,2] => [1,3] => [1,1] => [1,0,1,0] => 2
[2,2,2,2,2,1,1] => [5,2] => [1,1] => [1,0,1,0] => 2
[2,2,2,1,2,1,1,1] => [3,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[2,2,1,2,2,1,1,1] => [2,1,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,1,2,2,2,1,1,1] => [1,1,3,3] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,2,2,2,2,1,1,1] => [1,4,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,2,2,1,2,1,1,1,1] => [1,2,1,1,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,2,1,2,2,1,1,1,1] => [1,1,1,2,4] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,1,2,2,2,1,1,1,1] => [2,3,4] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,2,1,1,2,1,1,1,1,1] => [1,1,2,1,5] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,1,2,1,2,1,1,1,1,1] => [2,1,1,1,5] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,2,2,1,1,1,1,1] => [3,2,5] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,2,2,1] => [7,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,1,2,2,1,1,1] => [5,2,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,1,2,1,1,2,1] => [5,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,2,2,1,1,1,1,1,1,1] => [1,2,7] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,2,1,1,1,1,1,1,2,1] => [1,1,6,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,2,2,3,1,1] => [1,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,2,2,3,1,2,1] => [1,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,2,2,4,1,1,1] => [1,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[1,2,3,1,2,2,1] => [1,1,1,1,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,2,3,1,3,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,2,4,1,1,2,1] => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,2,3,2,2,1,1] => [1,1,1,2,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,2,3,3,1,1,1] => [1,1,2,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,2,4,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,2,5,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,3,1,2,2,2,1] => [1,1,1,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,3,1,3,2,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,3,2,1,3,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,4,1,1,2,2,1] => [1,1,2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,4,1,1,3,1,1] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,3,2,2,1,2,1] => [1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,3,3,1,1,2,1] => [1,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,4,2,1,1,2,1] => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,5,1,1,1,2,1] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,3,2,3,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,3,3,1,2,1,1] => [1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,3,4,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,4,1,2,2,1,1] => [1,1,1,2,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,4,1,3,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,5,1,1,2,1,1] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,4,2,2,1,1,1] => [1,1,2,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,4,3,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,5,2,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[1,6,1,1,1,1,1] => [1,1,5] => [2,1] => [1,1,0,0,1,0] => 2
[2,1,2,2,3,1,1] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[2,1,2,3,2,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[2,1,2,4,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[2,1,3,1,2,2,1] => [1,1,1,1,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[2,1,3,1,3,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[2,1,4,1,1,2,1] => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[2,1,3,2,2,1,1] => [1,1,1,2,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[2,1,3,3,1,1,1] => [1,1,2,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,1,4,1,2,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[2,1,4,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[2,1,5,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,2,1,2,3,1,1] => [2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[2,2,1,3,1,2,1] => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,2,1,3,2,1,1] => [2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[2,2,1,4,1,1,1] => [2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[3,1,1,2,2,2,1] => [1,2,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[3,1,1,3,1,2,1] => [1,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[3,1,1,3,2,1,1] => [1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[2,2,2,1,3,1,1] => [3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[2,3,1,1,2,2,1] => [1,1,2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[2,3,1,1,3,1,1] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[3,1,2,1,3,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[3,2,1,1,2,2,1] => [1,1,2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[3,2,1,1,3,1,1] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[4,1,1,1,2,2,1] => [1,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[4,1,1,1,3,1,1] => [1,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[2,2,3,1,1,2,1] => [2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[2,3,2,1,1,2,1] => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[2,4,1,1,1,2,1] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[3,1,2,2,1,2,1] => [1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[3,1,3,1,1,2,1] => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[4,1,1,2,1,2,1] => [1,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[3,2,2,1,1,2,1] => [1,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[3,3,1,1,1,2,1] => [2,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[4,1,2,1,1,2,1] => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[4,2,1,1,1,2,1] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[5,1,1,1,1,2,1] => [1,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,2,2,3,1,1,1] => [3,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,2,3,1,2,1,1] => [2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[2,2,3,2,1,1,1] => [2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[2,2,4,1,1,1,1] => [2,1,4] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,3,1,2,2,1,1] => [1,1,1,2,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[2,3,1,3,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[2,3,2,1,2,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[2,4,1,1,2,1,1] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[2,3,2,2,1,1,1] => [1,1,2,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,3,3,1,1,1,1] => [1,2,4] => [1,1,1] => [1,0,1,0,1,0] => 2
[2,4,1,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[2,4,2,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[2,5,1,1,1,1,1] => [1,1,5] => [2,1] => [1,1,0,0,1,0] => 2
[3,1,2,3,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[3,1,3,1,2,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[3,1,4,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[3,2,1,2,2,1,1] => [1,1,1,2,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[3,2,1,3,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[4,1,1,2,2,1,1] => [1,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => 2
[4,1,1,3,1,1,1] => [1,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[3,3,1,1,2,1,1] => [2,2,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[4,1,2,1,2,1,1] => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[4,2,1,1,2,1,1] => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[5,1,1,1,2,1,1] => [1,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
[3,2,2,2,1,1,1] => [1,3,3] => [1,2] => [1,0,1,1,0,0] => 2
[3,2,3,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[3,3,2,1,1,1,1] => [2,1,4] => [1,1,1] => [1,0,1,0,1,0] => 2
[3,4,1,1,1,1,1] => [1,1,5] => [2,1] => [1,1,0,0,1,0] => 2
[4,1,2,2,1,1,1] => [1,1,2,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[4,1,3,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[4,2,1,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[4,2,2,1,1,1,1] => [1,2,4] => [1,1,1] => [1,0,1,0,1,0] => 2
[4,3,1,1,1,1,1] => [1,1,5] => [2,1] => [1,1,0,0,1,0] => 2
[5,1,2,1,1,1,1] => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 2
[5,2,1,1,1,1,1] => [1,1,5] => [2,1] => [1,1,0,0,1,0] => 2
[6,1,1,1,1,1,1] => [1,6] => [1,1] => [1,0,1,0] => 2
[1,1,2,2,4,1] => [2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,3,1,1,1,5,1] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,3,1,1,4,1] => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,2,2,3,2,2,1] => [1,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[1,2,2,1,4,2,1] => [1,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,2,2,1,2,4,1] => [1,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,2,1,3,3,2,1] => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,5,2,1] => [1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,2,1,1,3,4,1] => [1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,2,1,1,1,6,1] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,5,1,3,1] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,4,3,2,1] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,4,1,4,1] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,3,1,5,1] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,2,5,2,1] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,2,3,4,1] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,2,1,6,1] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,7,1] => [5,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,2,1,1,1,1,1,1,1,1,1] => [1,1,9] => [2,1] => [1,1,0,0,1,0] => 2
[1,2,2,2,1,1,1,1,1] => [1,3,5] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,2,2,1,1,1,1,2,1] => [1,2,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,2,3,2,3] => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[2,2,2,2,4] => [4,1] => [1,1] => [1,0,1,0] => 2
[1,2,2,2,2,3] => [1,4,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,2,2,3,4] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,2,3,5] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,3,2,2,4] => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[5,1,1,1,1,2] => [1,4,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,1,2,1] => [8,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,2,1,1,1,1,1,2,1] => [1,1,5,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,1,1,3,1] => [7,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,3,1,1,1] => [5,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,1,5,1] => [5,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,2,1,2,1] => [5,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,3,1,1,1,1,1] => [3,1,5] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,3,1,3,1] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,5,1,1,1] => [3,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,7,1] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,4,1,2,1] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,2,1,2,1,1,1] => [3,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,2,1,4,1] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,2,1,1,1,2,1] => [3,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,2,3,2,1] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,3,1,1,1,1,1,1,1] => [1,1,7] => [2,1] => [1,1,0,0,1,0] => 2
[1,3,1,1,1,3,1] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,3,1,3,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,5,1,1,1,1,1] => [1,1,5] => [2,1] => [1,1,0,0,1,0] => 2
[1,7,1,1,1] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[1,4,1,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,4,1,1,1,2,1] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,2,1,1,1,1,1] => [1,1,1,1,5] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,2,1,4,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,2,1,1,1,2,1,1,1] => [1,1,3,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,2,1,1,1,4,1] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,3,2,1] => [1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,2,3,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,2,3,1,1,2,1] => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,2,2,1,2,2,1] => [1,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,5,1] => [7,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,3,1,3,1] => [5,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,5,1,1,1] => [5,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,1,4,1,2,1] => [5,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,2,1,4,1] => [5,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,2,3,2,1] => [5,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,3,1,1,1,3,1] => [3,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,3,1,3,1,1,1] => [3,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,5,1,1,1,1,1] => [3,1,5] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,7,1,1,1] => [3,1,3] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,9,1] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,1,6,1,2,1] => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,4,1,2,1,1,1] => [3,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,4,1,1,1,2,1] => [3,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,2,1,4,1,1,1] => [3,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,2,1,1,1,4,1] => [3,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,2,1,1,3,2,1] => [3,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,2,3,2,1,1,1] => [3,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,2,3,1,1,2,1] => [3,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,2,2,1,2,2,1] => [3,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[1,3,1,1,1,1,1,1,1,1,1] => [1,1,9] => [2,1] => [1,1,0,0,1,0] => 2
[1,3,1,1,1,1,1,3,1] => [1,1,5,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,3,1,1,1,3,1,1,1] => [1,1,3,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,3,1,3,1,1,1,1,1] => [1,1,1,1,5] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,3,1,5,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,5,1,1,1,1,1,1,1] => [1,1,7] => [2,1] => [1,1,0,0,1,0] => 2
[1,5,1,1,1,3,1] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,5,1,3,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,7,1,1,1,1,1] => [1,1,5] => [2,1] => [1,1,0,0,1,0] => 2
[1,9,1,1,1] => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 2
[1,6,1,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,6,1,1,1,2,1] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,4,1,2,1,1,1,1,1] => [1,1,1,1,5] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,4,1,4,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,4,1,1,1,2,1,1,1] => [1,1,3,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,4,1,1,1,4,1] => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,4,1,1,1,1,1,2,1] => [1,1,5,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,4,1,1,3,2,1] => [1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,4,3,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,4,3,1,1,2,1] => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,4,2,1,2,2,1] => [1,1,1,1,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,2,1,4,1,1,1,1,1] => [1,1,1,1,5] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,2,1,6,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,2,1,1,1,4,1,1,1] => [1,1,3,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,2,1,1,1,1,1,4,1] => [1,1,5,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,1,1,3,2,1] => [1,1,4,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,2,1,1,3,2,1,1,1] => [1,1,2,1,1,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,2,3,2,1,1,1,1,1] => [1,1,1,1,5] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,2,3,4,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,2,3,3,1,2,1] => [1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,2,3,1,1,2,1,1,1] => [1,1,1,2,1,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,2,3,1,1,1,1,2,1] => [1,1,1,4,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,2,5,2,1,1,1] => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,2,5,1,1,2,1] => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,2,4,1,2,2,1] => [1,1,1,1,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,2,2,1,2,2,1,1,1] => [1,2,1,2,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[1,2,2,1,1,1,2,2,1] => [1,2,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[1,1,9] => [2,1] => [1,1] => [1,0,1,0] => 2
[1,1,1,1,1,1,1,1,3] => [8,1] => [1,1] => [1,0,1,0] => 2
[2,2,2,2,1,1,2] => [4,2,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,2,2,1,2,3] => [2,2,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,2,2,2,1,1] => [4,3,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,1,2,2,2,3] => [3,3,1] => [2,1] => [1,1,0,0,1,0] => 2
[2,2,2,6] => [3,1] => [1,1] => [1,0,1,0] => 2
[2,2,6,2] => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,5,5] => [1,2] => [1,1] => [1,0,1,0] => 2
[1,2,1,2,1,1,1,1,1,1] => [1,1,1,1,6] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,2,1,1,1,1,1,2,1,1] => [1,1,5,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,1,2,1,1,1,1,1,2,1] => [2,1,5,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,2,1,2,1,1] => [5,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,1,1,2,1,2,1] => [6,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,2,2,2,4,1] => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[2,2,2,5,1] => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 2
[1,2,2,5,2] => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,1,2,1,1,1,2,1,1] => [2,1,3,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
[1,1,2,2,2,2,1] => [2,4,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,2,2,2,1,1,1] => [2,3,3] => [1,2] => [1,0,1,1,0,0] => 2
[1,1,2,2,3,1,1] => [2,2,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,1,2,2,1,2,1,1] => [2,2,1,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,1,2,3,2,1,1] => [2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,2,1,2,2,1,1] => [2,1,1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,1,3,2,2,1,1] => [2,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,1,1,2,2,2,1,1] => [3,3,2] => [2,1] => [1,1,0,0,1,0] => 2
[1,2,2,2,2,1,1] => [1,4,2] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,2,2,2,4] => [2,3,1] => [1,1,1] => [1,0,1,0,1,0] => 2
[1,1,2,2,1,1,1,1,1] => [2,2,5] => [2,1] => [1,1,0,0,1,0] => 2
[1,1,2,5,1,1] => [2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,5,2,1,1] => [2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,2,2,1,1] => [5,2,2] => [1,2] => [1,0,1,1,0,0] => 2
[1,4,2,2,1,1] => [1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[2,2,1,1,1,2,1,2] => [2,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,2,2,2,1,1,1,2] => [1,3,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[2,2,1,2,1,1,1,2] => [2,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[2,2,2,1,1,1,2,1] => [3,3,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 2
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Description
The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in 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 $C$.
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