Identifier
-
Mp00133:
Integer compositions
—delta morphism⟶
Integer compositions
Mp00039: Integer compositions —complement⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St000685: Dyck paths ⟶ ℤ
Values
[1] => [1] => [1] => [1,0] => 1
[1,1] => [2] => [1,1] => [1,0,1,0] => 2
[2] => [1] => [1] => [1,0] => 1
[1,1,1] => [3] => [1,1,1] => [1,0,1,0,1,0] => 3
[1,2] => [1,1] => [2] => [1,1,0,0] => 1
[2,1] => [1,1] => [2] => [1,1,0,0] => 1
[3] => [1] => [1] => [1,0] => 1
[1,1,1,1] => [4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,2] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[1,2,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,3] => [1,1] => [2] => [1,1,0,0] => 1
[2,1,1] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[2,2] => [2] => [1,1] => [1,0,1,0] => 2
[3,1] => [1,1] => [2] => [1,1,0,0] => 1
[4] => [1] => [1] => [1,0] => 1
[1,1,1,1,1] => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,2] => [3,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[1,1,2,1] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,3] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[1,2,1,1] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[1,2,2] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[1,3,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,4] => [1,1] => [2] => [1,1,0,0] => 1
[2,1,1,1] => [1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[2,1,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,2,1] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[2,3] => [1,1] => [2] => [1,1,0,0] => 1
[3,1,1] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[3,2] => [1,1] => [2] => [1,1,0,0] => 1
[4,1] => [1,1] => [2] => [1,1,0,0] => 1
[5] => [1] => [1] => [1,0] => 1
[1,1,1,1,1,1] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,1,2] => [4,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,2,1] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,3] => [3,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[1,1,2,1,1] => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,1,2,2] => [2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,3,1] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,4] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[1,2,1,1,1] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,2,1,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,2,2,1] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[1,2,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,3,1,1] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[1,3,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,4,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,5] => [1,1] => [2] => [1,1,0,0] => 1
[2,1,1,1,1] => [1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
[2,1,1,2] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[2,1,2,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,1,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,2,1,1] => [2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[2,2,2] => [3] => [1,1,1] => [1,0,1,0,1,0] => 3
[2,3,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,4] => [1,1] => [2] => [1,1,0,0] => 1
[3,1,1,1] => [1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[3,1,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[3,2,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[3,3] => [2] => [1,1] => [1,0,1,0] => 2
[4,1,1] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[4,2] => [1,1] => [2] => [1,1,0,0] => 1
[5,1] => [1,1] => [2] => [1,1,0,0] => 1
[6] => [1] => [1] => [1,0] => 1
[1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,1,1,2] => [5,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,2,1] => [4,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,3] => [4,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,2,1,1] => [3,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,2,2] => [3,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,3,1] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,4] => [3,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[1,1,2,1,1,1] => [2,1,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,2,1,2] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,2,2,1] => [2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
[1,1,2,3] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,3,1,1] => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,1,3,2] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,4,1] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,5] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[1,2,1,1,1,1] => [1,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,2,1,1,2] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,2,1,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,1,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,2,2,1,1] => [1,2,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
[1,2,2,2] => [1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[1,2,3,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,2,4] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,3,1,1,1] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,3,1,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,3,2,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,3,3] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[1,4,1,1] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[1,4,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,5,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,6] => [1,1] => [2] => [1,1,0,0] => 1
[2,1,1,1,1,1] => [1,5] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[2,1,1,1,2] => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[2,1,1,2,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,1,1,3] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[2,1,2,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[2,1,2,2] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
>>> Load all 1927 entries. <<<[2,1,3,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,1,4] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,2,1,1,1] => [2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[2,2,1,2] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[2,2,2,1] => [3,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[2,2,3] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[2,3,1,1] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[2,3,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,4,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,5] => [1,1] => [2] => [1,1,0,0] => 1
[3,1,1,1,1] => [1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
[3,1,1,2] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[3,1,2,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,1,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[3,2,1,1] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[3,2,2] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[3,3,1] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[3,4] => [1,1] => [2] => [1,1,0,0] => 1
[4,1,1,1] => [1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[4,1,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[4,2,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[4,3] => [1,1] => [2] => [1,1,0,0] => 1
[5,1,1] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[5,2] => [1,1] => [2] => [1,1,0,0] => 1
[6,1] => [1,1] => [2] => [1,1,0,0] => 1
[7] => [1] => [1] => [1,0] => 1
[1,1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,2,1] => [5,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,3] => [5,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,2,1,1] => [4,1,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,2,2] => [4,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,3,1] => [4,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,4] => [4,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,2,1,1,1] => [3,1,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,2,1,2] => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,2,2,1] => [3,2,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,2,3] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,3,1,1] => [3,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,3,2] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,4,1] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,5] => [3,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[1,1,2,1,1,1,1] => [2,1,4] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,2,1,1,2] => [2,1,2,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,2,1,2,1] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,2,1,3] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,2,2,1,1] => [2,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,2,2,2] => [2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[1,1,2,3,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,2,4] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,3,1,1,1] => [2,1,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,3,1,2] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,3,2,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,3,3] => [2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,4,1,1] => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,1,4,2] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,5,1] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,6] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[1,2,1,1,1,1,1] => [1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,2,1,1,1,2] => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,2,1,1,2,1] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,2,1,1,3] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,2,1,2,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,2,1,2,2] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,2,1,3,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,1,4] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,2,2,1,1,1] => [1,2,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,2,2,1,2] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,2,2,2,1] => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,2,2,3] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[1,2,3,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,2,3,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,2,4,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,2,5] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,3,1,1,1,1] => [1,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,3,1,1,2] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,3,1,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,3,1,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,3,2,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,3,2,2] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[1,3,3,1] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[1,3,4] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,4,1,1,1] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,4,1,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,4,2,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,4,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,5,1,1] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[1,5,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,6,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,7] => [1,1] => [2] => [1,1,0,0] => 1
[2,1,1,1,1,1,1] => [1,6] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[2,1,1,1,1,2] => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[2,1,1,1,2,1] => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[2,1,1,1,3] => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[2,1,1,2,1,1] => [1,2,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[2,1,1,2,2] => [1,2,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
[2,1,1,3,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,1,1,4] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[2,1,2,1,1,1] => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[2,1,2,1,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,1,2,2,1] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[2,1,2,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,1,3,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[2,1,3,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,1,4,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,1,5] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,2,1,1,1,1] => [2,4] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
[2,2,1,1,2] => [2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
[2,2,1,2,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,2,1,3] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[2,2,2,1,1] => [3,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[2,2,2,2] => [4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
[2,2,3,1] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[2,2,4] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[2,3,1,1,1] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[2,3,1,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,3,2,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,3,3] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[2,4,1,1] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[2,4,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,5,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,6] => [1,1] => [2] => [1,1,0,0] => 1
[3,1,1,1,1,1] => [1,5] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[3,1,1,1,2] => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[3,1,1,2,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[3,1,1,3] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[3,1,2,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[3,1,2,2] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[3,1,3,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,1,4] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[3,2,1,1,1] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[3,2,1,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,2,2,1] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[3,2,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[3,3,1,1] => [2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[3,3,2] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[3,4,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[3,5] => [1,1] => [2] => [1,1,0,0] => 1
[4,1,1,1,1] => [1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
[4,1,1,2] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[4,1,2,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[4,1,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[4,2,1,1] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[4,2,2] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[4,3,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[4,4] => [2] => [1,1] => [1,0,1,0] => 2
[5,1,1,1] => [1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[5,1,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[5,2,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[5,3] => [1,1] => [2] => [1,1,0,0] => 1
[6,1,1] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[6,2] => [1,1] => [2] => [1,1,0,0] => 1
[7,1] => [1,1] => [2] => [1,1,0,0] => 1
[8] => [1] => [1] => [1,0] => 1
[1,1,1,1,1,1,3] => [6,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,2,2] => [5,2] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,3,1] => [5,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,4] => [5,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,2,1,2] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,2,2,1] => [4,2,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,2,3] => [4,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,3,1,1] => [4,1,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,3,2] => [4,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,4,1] => [4,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,5] => [4,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,2,1,1,2] => [3,1,2,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,2,1,2,1] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,2,1,3] => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,2,2,1,1] => [3,2,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,2,2,2] => [3,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,2,3,1] => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,2,4] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,3,1,1,1] => [3,1,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,3,1,2] => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,3,2,1] => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,3,3] => [3,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,4,1,1] => [3,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,4,2] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,5,1] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,6] => [3,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[1,1,2,1,1,1,2] => [2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,2,1,1,2,1] => [2,1,2,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,2,1,1,3] => [2,1,2,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,2,1,2,1,1] => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,2,1,2,2] => [2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,2,1,3,1] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,2,1,4] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,2,2,1,1,1] => [2,2,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,2,2,1,2] => [2,2,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,2,2,2,1] => [2,3,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,2,2,3] => [2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
[1,1,2,3,1,1] => [2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,2,3,2] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,2,4,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,2,5] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,3,1,1,1,1] => [2,1,4] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,3,1,1,2] => [2,1,2,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,3,1,2,1] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,3,1,3] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,3,2,1,1] => [2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,3,2,2] => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,1,3,3,1] => [2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
[1,1,3,4] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,4,1,1,1] => [2,1,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,4,1,2] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,4,2,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,4,3] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,5,1,1] => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,1,5,2] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,6,1] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,7] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[1,2,1,1,1,1,2] => [1,1,4,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,2,1,1,1,2,1] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,2,1,1,1,3] => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,2,1,1,2,1,1] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[1,2,1,1,2,2] => [1,1,2,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,2,1,1,3,1] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,2,1,1,4] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,2,1,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,2,1,2,1,2] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,2,2,1] => [1,1,1,2,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,2,1,2,3] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,1,3,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,2,1,3,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,1,4,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,1,5] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,2,2,1,1,1,1] => [1,2,4] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,2,2,1,1,2] => [1,2,2,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,2,2,1,2,1] => [1,2,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,2,2,1,3] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,2,2,2,1,1] => [1,3,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,2,2,2,2] => [1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,2,2,3,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,2,2,4] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[1,2,3,1,1,1] => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,2,3,1,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,3,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,3,3] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[1,2,4,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,2,4,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,2,5,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,2,6] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,3,1,1,1,1,1] => [1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,3,1,1,1,2] => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,3,1,1,2,1] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,3,1,1,3] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,3,1,2,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,3,1,2,2] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,3,1,3,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,3,1,4] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,3,2,1,1,1] => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,3,2,1,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,3,2,2,1] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,3,2,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,3,3,1,1] => [1,2,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
[1,3,3,2] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[1,3,4,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,3,5] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,4,1,1,1,1] => [1,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,4,1,1,2] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,4,1,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,4,1,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,4,2,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,4,2,2] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[1,4,3,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,4,4] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[1,5,1,1,1] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,5,1,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,5,2,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,5,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,6,1,1] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[1,6,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,7,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,8] => [1,1] => [2] => [1,1,0,0] => 1
[2,1,1,1,1,1,2] => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[2,1,1,1,1,2,1] => [1,4,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[2,1,1,1,1,3] => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[2,1,1,1,2,1,1] => [1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[2,1,1,1,2,2] => [1,3,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[2,1,1,1,3,1] => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[2,1,1,1,4] => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[2,1,1,2,1,1,1] => [1,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,1,1,2,1,2] => [1,2,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,1,2,2,1] => [1,2,2,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[2,1,1,2,3] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,1,1,3,1,1] => [1,2,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[2,1,1,3,2] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,1,1,4,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,1,1,5] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[2,1,2,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[2,1,2,1,1,2] => [1,1,1,2,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[2,1,2,1,2,1] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,1,2,1,3] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,1,2,2,1,1] => [1,1,2,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[2,1,2,2,2] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[2,1,2,3,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,1,2,4] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,1,3,1,1,1] => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[2,1,3,1,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,3] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[2,1,4,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[2,1,4,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,1,5,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,1,6] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,2,1,1,1,1,1] => [2,5] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[2,2,1,1,1,2] => [2,3,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[2,2,1,1,2,1] => [2,2,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[2,2,1,1,3] => [2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
[2,2,1,2,1,1] => [2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[2,2,1,2,2] => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[2,2,1,3,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,2,1,4] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[2,2,2,1,1,1] => [3,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 3
[2,2,2,1,2] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[2,2,2,2,1] => [4,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[2,2,2,3] => [3,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[2,2,3,1,1] => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[2,2,3,2] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[2,2,4,1] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[2,2,5] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[2,3,1,1,1,1] => [1,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[2,3,1,1,2] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[2,3,1,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,3,1,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,3,2,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[2,3,2,2] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[2,3,3,1] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[2,3,4] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,4,1,1,1] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[2,4,1,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,4,2,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,4,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,5,1,1] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[2,5,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,6,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,7] => [1,1] => [2] => [1,1,0,0] => 1
[3,1,1,1,1,1,1] => [1,6] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[3,1,1,1,1,2] => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[3,1,1,1,2,1] => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[3,1,1,1,3] => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[3,1,1,2,1,1] => [1,2,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[3,1,1,2,2] => [1,2,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
[3,1,1,3,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[3,1,1,4] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[3,1,2,1,1,1] => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[3,1,2,1,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[3,1,2,2,1] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[3,1,2,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,1,3,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[3,1,3,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,1,4,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,1,5] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[3,2,1,1,1,1] => [1,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[3,2,1,1,2] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[3,2,1,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[3,2,1,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,2,2,1,1] => [1,2,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
[3,2,2,2] => [1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[3,2,3,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,2,4] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[3,3,1,1,1] => [2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[3,3,1,2] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[3,3,2,1] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[3,3,3] => [3] => [1,1,1] => [1,0,1,0,1,0] => 3
[3,4,1,1] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[3,4,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[3,5,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[3,6] => [1,1] => [2] => [1,1,0,0] => 1
[4,1,1,1,1,1] => [1,5] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[4,1,1,1,2] => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[4,1,1,2,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[4,1,1,3] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[4,1,2,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[4,1,2,2] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[4,1,3,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[4,1,4] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[4,2,1,1,1] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[4,2,1,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[4,2,2,1] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[4,2,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[4,3,1,1] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[4,3,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[4,4,1] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[4,5] => [1,1] => [2] => [1,1,0,0] => 1
[5,1,1,1,1] => [1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
[5,1,1,2] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[5,1,2,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[5,1,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[5,2,1,1] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[5,2,2] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[5,3,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[5,4] => [1,1] => [2] => [1,1,0,0] => 1
[6,1,1,1] => [1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[6,1,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[6,2,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[6,3] => [1,1] => [2] => [1,1,0,0] => 1
[7,1,1] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[7,2] => [1,1] => [2] => [1,1,0,0] => 1
[8,1] => [1,1] => [2] => [1,1,0,0] => 1
[9] => [1] => [1] => [1,0] => 1
[1,1,1,1,1,1,4] => [6,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,2,3] => [5,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,3,2] => [5,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,4,1] => [5,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,5] => [5,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,2,1,3] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,2,2,2] => [4,3] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,1,2,3,1] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,2,4] => [4,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,3,1,2] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,3,2,1] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,3,3] => [4,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,4,1,1] => [4,1,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,4,2] => [4,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,5,1] => [4,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,6] => [4,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,2,1,1,3] => [3,1,2,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,2,1,2,2] => [3,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,2,1,3,1] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,2,1,4] => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,2,2,1,2] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,2,2,2,1] => [3,3,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,2,2,3] => [3,2,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,2,3,1,1] => [3,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,2,3,2] => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,2,4,1] => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,2,5] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,3,1,1,2] => [3,1,2,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,3,1,2,1] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,3,1,3] => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,3,2,1,1] => [3,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,3,2,2] => [3,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,3,3,1] => [3,2,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,3,4] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,4,1,1,1] => [3,1,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,4,1,2] => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,4,2,1] => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,4,3] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,5,1,1] => [3,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,5,2] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,6,1] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,7] => [3,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[1,1,2,1,1,1,3] => [2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,2,1,1,2,2] => [2,1,2,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,2,1,1,3,1] => [2,1,2,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,2,1,1,4] => [2,1,2,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,2,1,2,1,2] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,2,1,2,2,1] => [2,1,1,2,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,2,1,2,3] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,2,1,3,1,1] => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,2,1,3,2] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,2,1,4,1] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,2,1,5] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,2,2,1,1,2] => [2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,2,2,1,2,1] => [2,2,1,1,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,2,2,1,3] => [2,2,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,2,2,2,1,1] => [2,3,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,2,2,2,2] => [2,4] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,2,2,3,1] => [2,2,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,2,2,4] => [2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
[1,1,2,3,1,1,1] => [2,1,1,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,2,3,1,2] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,2,3,2,1] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,2,3,3] => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,1,2,4,1,1] => [2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,2,4,2] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,2,5,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,2,6] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,3,1,1,1,2] => [2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,3,1,1,2,1] => [2,1,2,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,3,1,1,3] => [2,1,2,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,3,1,2,1,1] => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,3,1,2,2] => [2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,3,1,3,1] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,3,1,4] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,3,2,1,1,1] => [2,1,1,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,3,2,1,2] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,3,2,2,1] => [2,1,2,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,3,2,3] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,3,3,1,1] => [2,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,3,3,2] => [2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
[1,1,3,4,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,3,5] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,4,1,1,1,1] => [2,1,4] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,4,1,1,2] => [2,1,2,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,4,1,2,1] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,4,1,3] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,4,2,1,1] => [2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,4,2,2] => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,1,4,3,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,4,4] => [2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,5,1,1,1] => [2,1,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,5,1,2] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,5,2,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,5,3] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,6,1,1] => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,1,6,2] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,7,1] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,8] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[1,2,1,1,1,1,3] => [1,1,4,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,2,1,1,1,2,2] => [1,1,3,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,2,1,1,1,3,1] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,2,1,1,1,4] => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,2,1,1,2,1,2] => [1,1,2,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,2,1,1,2,2,1] => [1,1,2,2,1] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,2,1,1,2,3] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,2,1,1,3,1,1] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[1,2,1,1,3,2] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,2,1,1,4,1] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,2,1,1,5] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,2,1,2,1,1,2] => [1,1,1,1,2,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,2,1,2,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,2,1,2,1,3] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,2,2,1,1] => [1,1,1,2,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,2,1,2,2,2] => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,2,1,2,3,1] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,2,4] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,1,3,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,2,1,3,1,2] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,3,2,1] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,3,3] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,2,1,4,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,2,1,4,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,1,5,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,1,6] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,2,2,1,1,1,2] => [1,2,3,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,2,2,1,1,2,1] => [1,2,2,1,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,2,2,1,1,3] => [1,2,2,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,2,2,1,2,1,1] => [1,2,1,1,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,2,2,1,2,2] => [1,2,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,2,2,1,3,1] => [1,2,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,2,2,1,4] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,2,2,2,1,1,1] => [1,3,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,2,2,2,1,2] => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,2,2,2,2,1] => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,2,2,2,3] => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,2,2,3,1,1] => [1,2,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,2,2,3,2] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,2,2,4,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,2,2,5] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[1,2,3,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,2,3,1,1,2] => [1,1,1,2,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,2,3,1,2,1] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,1,3] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,3,2,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,2,3,2,2] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,2,3,3,1] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,2,3,4] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,2,4,1,1,1] => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,2,4,1,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,2,5,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,2,5,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,2,6,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,2,7] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,3,1,1,1,1,2] => [1,1,4,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,3,1,1,1,2,1] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,3,1,1,1,3] => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,3,1,1,2,1,1] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[1,3,1,1,2,2] => [1,1,2,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,3,1,1,3,1] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,3,1,1,4] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,3,1,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,3,1,2,1,2] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,1,2,2,1] => [1,1,1,2,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,3,1,2,3] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,3,1,3,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,3,1,3,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,3,1,4,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,3,1,5] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,3,2,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,3,2,1,1,2] => [1,1,1,2,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,3,2,1,2,1] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,1,3] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,3,2,2,1,1] => [1,1,2,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,3,2,2,2] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,3,2,3,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,3,2,4] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,3,3,1,1,1] => [1,2,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,3,3,1,2] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,3,3,2,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,3,3,3] => [1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[1,3,4,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,3,4,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,3,5,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,3,6] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,4,1,1,1,1,1] => [1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,4,1,1,1,2] => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,4,1,1,2,1] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,4,1,1,3] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,4,1,2,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,4,1,2,2] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,4,1,3,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,4,1,4] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,4,2,1,1,1] => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,4,2,1,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,4,2,2,1] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,4,2,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,4,3,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,4,3,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,4,4,1] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[1,4,5] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,5,1,1,1,1] => [1,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,5,1,1,2] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,5,1,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,5,1,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,5,2,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,5,2,2] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[1,5,3,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,5,4] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,6,1,1,1] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,6,1,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,6,2,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,6,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,7,1,1] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[1,7,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,8,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,9] => [1,1] => [2] => [1,1,0,0] => 1
[2,1,1,1,1,1,3] => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[2,1,1,1,1,2,2] => [1,4,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[2,1,1,1,1,3,1] => [1,4,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[2,1,1,1,1,4] => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[2,1,1,1,2,1,2] => [1,3,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[2,1,1,1,2,2,1] => [1,3,2,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[2,1,1,1,2,3] => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[2,1,1,1,3,1,1] => [1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[2,1,1,1,3,2] => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[2,1,1,1,4,1] => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[2,1,1,1,5] => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[2,1,1,2,1,1,2] => [1,2,1,2,1] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[2,1,1,2,1,2,1] => [1,2,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,1,2,1,3] => [1,2,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,1,2,2,1,1] => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[2,1,1,2,2,2] => [1,2,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[2,1,1,2,3,1] => [1,2,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,1,2,4] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,1,1,3,1,1,1] => [1,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,1,1,3,1,2] => [1,2,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,1,3,2,1] => [1,2,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,1,3,3] => [1,2,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
[2,1,1,4,1,1] => [1,2,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[2,1,1,4,2] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,1,1,5,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,1,1,6] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[2,1,2,1,1,1,2] => [1,1,1,3,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[2,1,2,1,1,2,1] => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[2,1,2,1,1,3] => [1,1,1,2,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[2,1,2,1,2,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,1,2,1,2,2] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,1,2,1,3,1] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,1,2,1,4] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,1,2,2,1,1,1] => [1,1,2,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[2,1,2,2,1,2] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[2,1,2,2,2,1] => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[2,1,2,2,3] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[2,1,2,3,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,1,2,3,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,1,2,4,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,1,2,5] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,1,3,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[2,1,3,1,1,2] => [1,1,1,2,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[2,1,3,1,2,1] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,1,3,1,3] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,2,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,1,3,2,2] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[2,1,3,3,1] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[2,1,3,4] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,1,4,1,1,1] => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[2,1,4,1,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,1,4,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,1,5,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[2,1,5,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,1,6,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,1,7] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,2,1,1,1,1,2] => [2,4,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[2,2,1,1,1,2,1] => [2,3,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[2,2,1,1,1,3] => [2,3,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[2,2,1,1,2,1,1] => [2,2,1,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[2,2,1,1,2,2] => [2,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,2,1,1,3,1] => [2,2,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[2,2,1,1,4] => [2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
[2,2,1,2,1,1,1] => [2,1,1,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[2,2,1,2,1,2] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,2,1,2,2,1] => [2,1,2,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[2,2,1,2,3] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,2,1,3,1,1] => [2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[2,2,1,3,2] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,2,1,4,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,2,1,5] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[2,2,2,1,1,1,1] => [3,4] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 3
[2,2,2,1,1,2] => [3,2,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[2,2,2,1,2,1] => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[2,2,2,1,3] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[2,2,2,2,1,1] => [4,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[2,2,2,2,2] => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
[2,2,2,3,1] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[2,2,2,4] => [3,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[2,2,3,1,1,1] => [2,1,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,2,3,1,2] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,2,3,2,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,2,3,3] => [2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[2,2,4,1,1] => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[2,2,4,2] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[2,2,5,1] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[2,2,6] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[2,3,1,1,1,1,1] => [1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[2,3,1,1,1,2] => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[2,3,1,1,2,1] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[2,3,1,1,3] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[2,3,1,2,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,3,1,2,2] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[2,3,1,3,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,3,1,4] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,3,2,1,1,1] => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[2,3,2,1,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,3,2,2,1] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[2,3,2,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,3,3,1,1] => [1,2,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
[2,3,3,2] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[2,3,4,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,3,5] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,4,1,1,1,1] => [1,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[2,4,1,1,2] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[2,4,1,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,4,1,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,4,2,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[2,4,2,2] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[2,4,3,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,4,4] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[2,5,1,1,1] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[2,5,1,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,5,2,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,5,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,6,1,1] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[2,6,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,7,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,8] => [1,1] => [2] => [1,1,0,0] => 1
[3,1,1,1,1,1,2] => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[3,1,1,1,1,2,1] => [1,4,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[3,1,1,1,1,3] => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[3,1,1,1,2,1,1] => [1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[3,1,1,1,2,2] => [1,3,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[3,1,1,1,3,1] => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[3,1,1,1,4] => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[3,1,1,2,1,1,1] => [1,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[3,1,1,2,1,2] => [1,2,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[3,1,1,2,2,1] => [1,2,2,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[3,1,1,2,3] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[3,1,1,3,1,1] => [1,2,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[3,1,1,3,2] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[3,1,1,4,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[3,1,1,5] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[3,1,2,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[3,1,2,1,1,2] => [1,1,1,2,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[3,1,2,1,2,1] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,1,2,1,3] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[3,1,2,2,1,1] => [1,1,2,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[3,1,2,2,2] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[3,1,2,3,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[3,1,2,4] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,1,3,1,1,1] => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[3,1,3,1,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[3,1,3,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[3,1,3,3] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[3,1,4,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[3,1,4,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,1,5,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,1,6] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[3,2,1,1,1,1,1] => [1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[3,2,1,1,1,2] => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[3,2,1,1,2,1] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,2,1,1,3] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[3,2,1,2,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[3,2,1,2,2] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[3,2,1,3,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[3,2,1,4] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,2,2,1,1,1] => [1,2,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[3,2,2,1,2] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[3,2,2,2,1] => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[3,2,2,3] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[3,2,3,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[3,2,3,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,2,4,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,2,5] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[3,3,1,1,1,1] => [2,4] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
[3,3,1,1,2] => [2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
[3,3,1,2,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[3,3,1,3] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[3,3,2,1,1] => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[3,3,2,2] => [2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[3,3,3,1] => [3,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[3,3,4] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[3,4,1,1,1] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[3,4,1,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,4,2,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,4,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[3,5,1,1] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[3,5,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[3,6,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[3,7] => [1,1] => [2] => [1,1,0,0] => 1
[4,1,1,1,1,1,1] => [1,6] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[4,1,1,1,1,2] => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[4,1,1,1,2,1] => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[4,1,1,1,3] => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[4,1,1,2,1,1] => [1,2,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[4,1,1,2,2] => [1,2,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
[4,1,1,3,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[4,1,1,4] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[4,1,2,1,1,1] => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[4,1,2,1,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[4,1,2,2,1] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[4,1,2,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[4,1,3,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[4,1,3,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[4,1,4,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[4,1,5] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[4,2,1,1,1,1] => [1,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[4,2,1,1,2] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[4,2,1,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[4,2,1,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[4,2,2,1,1] => [1,2,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
[4,2,2,2] => [1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[4,2,3,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[4,2,4] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[4,3,1,1,1] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[4,3,1,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[4,3,2,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[4,3,3] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[4,4,1,1] => [2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[4,4,2] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[4,5,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[4,6] => [1,1] => [2] => [1,1,0,0] => 1
[5,1,1,1,1,1] => [1,5] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[5,1,1,1,2] => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[5,1,1,2,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[5,1,1,3] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[5,1,2,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[5,1,2,2] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[5,1,3,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[5,1,4] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[5,2,1,1,1] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[5,2,1,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[5,2,2,1] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[5,2,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[5,3,1,1] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[5,3,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[5,4,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[5,5] => [2] => [1,1] => [1,0,1,0] => 2
[6,1,1,1,1] => [1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
[6,1,1,2] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[6,1,2,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[6,1,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[6,2,1,1] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[6,2,2] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[6,3,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[6,4] => [1,1] => [2] => [1,1,0,0] => 1
[7,1,1,1] => [1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[7,1,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[7,2,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[7,3] => [1,1] => [2] => [1,1,0,0] => 1
[8,1,1] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[8,2] => [1,1] => [2] => [1,1,0,0] => 1
[9,1] => [1,1] => [2] => [1,1,0,0] => 1
[10] => [1] => [1] => [1,0] => 1
[1,10] => [1,1] => [2] => [1,1,0,0] => 1
[1,8,1,1] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[1,7,2,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,6,3,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,5,4,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,4,5,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,3,6,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,2,7,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,1,8,1] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[10,1] => [1,1] => [2] => [1,1,0,0] => 1
[1,1,1,1,4,4] => [4,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,2,2,3,3] => [2,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,2,1,3,4] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,3,3,2,2] => [2,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,3,2,2,3] => [2,1,2,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,3,1,2,4] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,4,4,1,1] => [2,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,4,3,1,2] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,4,2,1,3] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,4,1,1,4] => [2,1,2,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,5,5] => [2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[2,2,1,1,3,3] => [2,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,2,2,2,2,2] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[2,2,2,1,2,3] => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[2,2,3,3,1,1] => [2,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,2,3,2,1,2] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,2,3,1,1,3] => [2,1,2,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[2,2,4,4] => [2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[2,1,1,2,3,3] => [1,2,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[2,1,1,1,3,4] => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[2,1,2,3,2,2] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,1,2,2,2,3] => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[2,1,2,1,2,4] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,1,3,4,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,1,3,3,1,2] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[2,1,3,2,1,3] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,1,3,1,1,4] => [1,1,1,2,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[2,1,4,5] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,3,1,1,2,2] => [2,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[3,3,2,2,1,1] => [2,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[3,3,2,1,1,2] => [2,1,2,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[3,3,3,3] => [4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
[3,2,1,2,2,2] => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[3,2,1,1,2,3] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,2,2,3,1,1] => [1,2,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[3,2,2,2,1,2] => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[3,2,2,1,1,3] => [1,2,2,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[3,2,3,4] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,1,1,3,2,2] => [1,2,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[3,1,1,2,2,3] => [1,2,2,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[3,1,1,1,2,4] => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[3,1,2,4,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[3,1,2,3,1,2] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,1,2,2,1,3] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,1,2,1,1,4] => [1,1,1,2,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[3,1,3,5] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[4,4,1,1,1,1] => [2,4] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
[4,4,2,2] => [2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[4,3,1,2,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[4,3,1,1,1,2] => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[4,3,2,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[4,2,1,3,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[4,2,1,2,1,2] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[4,2,1,1,1,3] => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[4,2,2,4] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[4,1,1,4,1,1] => [1,2,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[4,1,1,3,1,2] => [1,2,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[4,1,1,2,1,3] => [1,2,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[4,1,1,1,1,4] => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[4,1,2,5] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[5,5,1,1] => [2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[5,4,1,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[5,3,1,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[5,2,1,4] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[5,1,1,5] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[6,6] => [2] => [1,1] => [1,0,1,0] => 2
[1,2,2,2,2,2,1] => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,2,2,2,3,2] => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,2,2,3,3,1] => [1,2,2,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,2,2,3,2,2] => [1,2,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,2,2,4,3] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,2,3,3,2,1] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,2,3,4,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,3,2,3,1] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,3,2,2,2] => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,2,3,3,3] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,2,4,4,1] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,2,4,3,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,2,3] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,4] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,3,3,2,2,1] => [1,2,2,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,3,3,3,2] => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,3,4,3,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,3,4,2,2] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,3,5,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,3,2,3,2,1] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,3,2,4,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,3,2,2,3,1] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,3,2,2,2,2] => [1,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,3,2,3,3] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,3,3,4,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,3,3,2,3] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,3,4,4] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[1,4,4,2,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,4,5,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,4,3,3,1] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,4,3,2,2] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,4,4,3] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[1,4,2,4,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,4,2,3,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,4,2,2,3] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,4,3,4] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,5,5,1] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[1,5,4,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,5,3,3] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[1,5,2,4] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,6,5] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,3,2,2,2,1] => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[2,3,2,3,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,3,3,3,1] => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[2,3,3,2,2] => [1,2,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
[2,3,4,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,4,3,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,4,4,2] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[2,4,2,3,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,4,2,2,2] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[2,4,3,3] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[2,5,4,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,5,3,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,5,2,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,6,4] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,2,3,2,2,1] => [2,1,2,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[2,2,3,3,2] => [2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
[2,2,4,3,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,2,4,2,2] => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[2,2,5,3] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[2,2,2,3,2,1] => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[2,2,2,4,2] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[2,2,2,2,3,1] => [4,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[2,2,2,3,3] => [3,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[2,2,3,4,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,2,3,2,3] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,3,4,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,3,5,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,3,2,4,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,3,2,2,3] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[2,3,3,4] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[2,4,5,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,4,2,4] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,5,5] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[3,4,2,2,1] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[3,4,3,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,5,3,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,5,2,2] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[3,6,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[3,3,3,2,1] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[3,3,4,2] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[3,3,2,3,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[3,3,2,2,2] => [2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[3,4,4,1] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[3,4,2,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,5,4] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[3,2,4,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[3,2,5,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,2,3,3,1] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[3,2,3,2,2] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[3,2,4,3] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[3,2,2,4,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[3,2,2,3,2] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[3,2,2,2,3] => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[3,3,5,1] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[3,3,2,4] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[3,4,5] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[4,5,2,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[4,6,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[4,4,3,1] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[4,5,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[4,3,4,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[4,3,3,2] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[4,4,4] => [3] => [1,1,1] => [1,0,1,0,1,0] => 3
[4,2,5,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[4,2,4,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[4,2,3,3] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[4,3,5] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[5,6,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[5,5,2] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[5,4,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[5,3,4] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[5,2,5] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,8,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,7,1,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,6,1,1,2] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,5,1,1,1,2] => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,4,1,1,1,1,2] => [1,1,4,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,11] => [1,1] => [2] => [1,1,0,0] => 1
[1,9,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,7,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,8,1,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,6,2,2] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[1,7,1,1,2] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,5,2,1,2] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,6,1,1,1,2] => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,4,2,1,1,2] => [1,1,1,2,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,5,1,1,1,1,2] => [1,1,4,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,3,2,1,1,1,2] => [1,1,1,3,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,2,2,2,2,2] => [1,5] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,2,2,2,1,3] => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,2,2,1,3,2] => [1,2,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,2,2,1,2,3] => [1,2,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,2,2,1,1,4] => [1,2,2,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,2,1,3,2,2] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,2,1,3,1,3] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,2,3,2] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,2,2,3] => [1,1,1,2,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,2,1,2,1,4] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,1,1,4,2] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,2,1,1,3,3] => [1,1,2,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,2,1,1,2,4] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,2,1,1,1,5] => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,3,2,2,2] => [2,1,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,3,2,1,3] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,3,1,3,2] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,3,1,2,3] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,3,1,1,4] => [2,1,2,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,2,3,2,2] => [2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,2,3,1,3] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,2,2,3,2] => [2,2,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,2,2,2,3] => [2,3,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,2,2,1,4] => [2,2,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,2,1,4,2] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,2,1,3,3] => [2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,2,1,2,4] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,2,1,1,5] => [2,1,2,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,4,2,2] => [3,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,4,1,3] => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,3,3,2] => [3,2,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,3,2,3] => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,3,1,4] => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,2,4,2] => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,2,3,3] => [3,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,2,2,4] => [3,2,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,2,1,5] => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,5,2] => [4,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,4,3] => [4,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,3,4] => [4,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,2,5] => [4,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,6] => [5,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,2,2,2,2,2,2] => [1,6] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,2,2,2,2,1,3] => [1,4,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,2,2,2,1,3,2] => [1,3,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,2,2,1,2,3] => [1,3,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,2,2,2,1,1,4] => [1,3,2,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,2,2,1,3,2,2] => [1,2,1,1,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,2,2,1,3,1,3] => [1,2,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,2,1,2,3,2] => [1,2,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,2,1,2,2,3] => [1,2,1,2,1] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,2,2,1,2,1,4] => [1,2,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,2,1,1,4,2] => [1,2,2,1,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,2,2,1,1,3,3] => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,2,2,1,1,2,4] => [1,2,2,1,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,2,2,1,1,1,5] => [1,2,3,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,2,1,3,2,2,2] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,2,1,3,2,1,3] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,2,1,3,1,3,2] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,2,1,3,1,2,3] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,2,1,3,1,1,4] => [1,1,1,1,2,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,2,1,2,3,2,2] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,2,1,2,3,1,3] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,2,1,2,2,3,2] => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,2,1,2,2,2,3] => [1,1,1,3,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,2,1,2,2,1,4] => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,2,1,2,1,4,2] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,2,1,2,1,3,3] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,2,1,2,1,2,4] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,2,1,2,1,1,5] => [1,1,1,1,2,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,2,1,1,4,2,2] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[1,2,1,1,4,1,3] => [1,1,2,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,2,1,1,3,3,2] => [1,1,2,2,1] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,2,1,1,3,2,3] => [1,1,2,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,2,1,1,3,1,4] => [1,1,2,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,2,1,1,2,4,2] => [1,1,2,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,2,1,1,2,3,3] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[1,2,1,1,2,2,4] => [1,1,2,2,1] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,2,1,1,2,1,5] => [1,1,2,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,2,1,1,1,5,2] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,2,1,1,1,4,3] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,2,1,1,1,3,4] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,2,1,1,1,2,5] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,2,1,1,1,1,6] => [1,1,4,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,3,2,2,2,2] => [2,1,4] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,3,2,2,1,3] => [2,1,2,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,3,2,1,3,2] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,3,2,1,2,3] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,3,2,1,1,4] => [2,1,1,2,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,3,1,3,2,2] => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,3,1,3,1,3] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,3,1,2,3,2] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,3,1,2,2,3] => [2,1,1,2,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,3,1,2,1,4] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,3,1,1,4,2] => [2,1,2,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,3,1,1,3,3] => [2,1,2,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,3,1,1,2,4] => [2,1,2,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,3,1,1,1,5] => [2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,2,3,2,2,2] => [2,1,1,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,2,3,2,1,3] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,2,3,1,3,2] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,2,3,1,2,3] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,2,3,1,1,4] => [2,1,1,2,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,2,2,3,2,2] => [2,2,1,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,2,2,3,1,3] => [2,2,1,1,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,2,2,2,3,2] => [2,3,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,2,2,2,2,3] => [2,4,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,2,2,2,1,4] => [2,3,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,2,2,1,4,2] => [2,2,1,1,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,2,2,1,3,3] => [2,2,1,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,2,2,1,2,4] => [2,2,1,1,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,2,2,1,1,5] => [2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,2,1,4,2,2] => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,2,1,4,1,3] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,2,1,3,3,2] => [2,1,1,2,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,2,1,3,2,3] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,2,1,3,1,4] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,2,1,2,4,2] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,2,1,2,3,3] => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,2,1,2,2,4] => [2,1,1,2,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,2,1,2,1,5] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,2,1,1,5,2] => [2,1,2,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,2,1,1,4,3] => [2,1,2,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,2,1,1,3,4] => [2,1,2,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,2,1,1,2,5] => [2,1,2,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,2,1,1,1,6] => [2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,4,2,2,2] => [3,1,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,4,2,1,3] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,4,1,3,2] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,4,1,2,3] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,4,1,1,4] => [3,1,2,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,3,3,2,2] => [3,2,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,3,3,1,3] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,3,2,3,2] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,3,2,2,3] => [3,1,2,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,3,2,1,4] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,3,1,4,2] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,3,1,3,3] => [3,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,3,1,2,4] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,3,1,1,5] => [3,1,2,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,2,4,2,2] => [3,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,2,4,1,3] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,2,3,3,2] => [3,1,2,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,2,3,2,3] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,2,3,1,4] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,2,2,4,2] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,2,2,3,3] => [3,2,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,2,2,2,4] => [3,3,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,2,2,1,5] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,2,1,5,2] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,2,1,4,3] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,2,1,3,4] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,2,1,2,5] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,2,1,1,6] => [3,1,2,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,5,2,2] => [4,1,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,5,1,3] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,4,3,2] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,4,2,3] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,4,1,4] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,3,4,2] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,3,3,3] => [4,3] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,1,3,2,4] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,3,1,5] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,2,5,2] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,2,4,3] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,2,3,4] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,2,2,5] => [4,2,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,2,1,6] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,6,2] => [5,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,5,3] => [5,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,4,4] => [5,2] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,3,5] => [5,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,2,6] => [5,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,7] => [6,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[12] => [1] => [1] => [1,0] => 1
[1,2,9] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[3,2,7] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,4,7] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,1,2,1,7] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,2,2,2,5] => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,1,2,3,5] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[3,1,2,1,5] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,3,2,1,5] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,4,1,5] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,2,1,1,5] => [3,1,2,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[7,2,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,1,2,1,2,2,3] => [2,1,1,2,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,8,3] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,1,2,5,3] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[3,1,2,3,3] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,4,3,3] => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,2,1,3,3] => [3,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[5,1,2,1,3] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,2,1,2,1,3] => [1,2,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[3,3,2,1,3] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,5,2,1,3] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,2,2,2,1,3] => [2,3,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[3,1,4,1,3] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,3,4,1,3] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,6,1,3] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,2,3,1,3] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[3,1,1,2,1,1,3] => [1,2,1,2,1] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,3,1,2,1,1,3] => [1,1,1,1,2,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,3,2,1,1,3] => [2,1,1,2,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,4,1,1,3] => [3,1,2,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[9,2,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,2,6,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,2,1,4,2,1] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[5,2,2,2,1] => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,6,2,2,1] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,1,2,3,2,2,1] => [2,1,1,2,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[3,1,2,1,2,2,1] => [1,1,1,1,2,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,3,2,1,2,2,1] => [1,1,1,1,2,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,4,1,2,2,1] => [2,1,1,2,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[7,4,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,1,2,1,2,4,1] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,2,2,6,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[3,8,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,10,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,1,2,7,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[3,1,2,5,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,3,2,5,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,4,5,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,2,1,5,1] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[5,1,2,3,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,2,1,2,3,1] => [1,2,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,5,2,3,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,2,2,2,3,1] => [2,3,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[3,1,4,3,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,6,3,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,2,3,3,1] => [3,1,2,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[3,1,1,2,1,3,1] => [1,2,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,1,2,1,3,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,3,2,1,3,1] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,4,1,3,1] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[7,1,2,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,2,4,1,2,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[3,2,2,1,2,1,1] => [1,2,1,1,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,4,2,1,2,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[5,3,2,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,2,2,3,2,1,1] => [1,2,1,1,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[3,5,2,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,7,2,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,2,4,2,1,1] => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[3,1,2,2,2,1,1] => [1,1,3,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,3,2,2,2,1,1] => [1,1,3,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,4,2,2,1,1] => [2,1,2,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[5,1,4,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,2,2,1,4,1,1] => [1,2,1,1,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[3,3,4,1,1] => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,5,4,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,2,2,4,1,1] => [2,2,1,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[3,1,6,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,3,6,1,1] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,8,1,1] => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,2,5,1,1] => [3,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[3,1,1,2,3,1,1] => [1,2,1,1,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,3,1,2,3,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,3,2,3,1,1] => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,4,3,1,1] => [3,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[5,1,1,2,1,1,1] => [1,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[3,3,1,2,1,1,1] => [2,1,1,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,5,1,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[3,1,3,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,3,3,2,1,1,1] => [1,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,5,2,1,1,1] => [2,1,1,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[3,1,1,4,1,1,1] => [1,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,3,1,4,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,3,4,1,1,1] => [2,1,1,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,6,1,1,1] => [3,1,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,2,2,2,1,2,1] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[2,2,2,1,2,1,2] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,2,2,1,2,2,1] => [3,1,2,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[2,2,2,1,1,2,2] => [3,2,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,2,1,2,1,2,2] => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,2,1,2,2,1,2] => [2,1,2,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[2,2,1,2,2,2,1] => [2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[2,2,1,1,2,2,2] => [2,2,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[2,1,2,1,2,2,2] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[2,1,2,2,1,2,2] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[2,1,2,2,2,1,2] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[2,1,2,2,2,2,1] => [1,1,4,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[2,1,1,2,2,2,2] => [1,2,4] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,2,1,2,2,2,2] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,2,2,1,2,2,2] => [1,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,2,2,2,1,2,2] => [1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,2,2,2,2,1,2] => [1,4,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,2,2,2,2,2] => [2,5] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[3,3,3,2] => [3,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[3,4,4] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[2,3,3,3] => [1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[4,4,3] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[3,2,2,2,2,1] => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[4,3,2,2,1] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[4,2,3,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[4,2,2,3,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[4,2,2,2,2] => [1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
[5,4,2,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[5,3,3,1] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[5,3,2,2] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[5,2,4,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[5,2,3,2] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[5,2,2,3] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[6,5,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[6,4,2] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[6,3,3] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[6,2,4] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[7,5] => [1,1] => [2] => [1,1,0,0] => 1
[2,8,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,1,7,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,1,1,6,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,1,1,1,5,1] => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[2,1,1,1,1,4,1] => [1,4,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[11,1] => [1,1] => [2] => [1,1,0,0] => 1
[2,9,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[3,7,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[2,1,8,1] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[2,2,6,1] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[2,1,1,7,1] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,1,2,5,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,1,1,1,6,1] => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[2,1,1,2,4,1] => [1,2,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,1,1,1,5,1] => [1,4,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[2,1,1,1,2,3,1] => [1,3,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[2,2,2,2,2,1] => [5,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[3,1,2,2,2,1] => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[2,3,1,2,2,1] => [1,1,1,2,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[3,2,1,2,2,1] => [1,1,1,2,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[4,1,1,2,2,1] => [1,2,2,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[2,2,3,1,2,1] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[3,1,3,1,2,1] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,3,2,1,2,1] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,2,2,1,2,1] => [1,2,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[4,1,2,1,2,1] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,4,1,1,2,1] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,3,1,1,2,1] => [2,2,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[4,2,1,1,2,1] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[5,1,1,1,2,1] => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[2,2,2,3,1,1] => [3,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[3,1,2,3,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,3,1,3,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[3,2,1,3,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[4,1,1,3,1,1] => [1,2,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[2,2,3,2,1,1] => [2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[3,1,3,2,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,3,2,2,1,1] => [1,1,2,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[3,2,2,2,1,1] => [1,3,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[4,1,2,2,1,1] => [1,1,2,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[2,4,1,2,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[3,3,1,2,1,1] => [2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[4,2,1,2,1,1] => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[5,1,1,2,1,1] => [1,2,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[2,2,4,1,1,1] => [2,1,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[3,1,4,1,1,1] => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[2,3,3,1,1,1] => [1,2,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[3,2,3,1,1,1] => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[4,1,3,1,1,1] => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[2,4,2,1,1,1] => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[3,3,2,1,1,1] => [2,1,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[4,2,2,1,1,1] => [1,2,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[5,1,2,1,1,1] => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[2,5,1,1,1,1] => [1,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[3,4,1,1,1,1] => [1,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[4,3,1,1,1,1] => [1,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[5,2,1,1,1,1] => [1,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[6,1,1,1,1,1] => [1,5] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[2,2,2,2,2,2,1] => [6,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[3,1,2,2,2,2,1] => [1,1,4,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[2,3,1,2,2,2,1] => [1,1,1,3,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[3,2,1,2,2,2,1] => [1,1,1,3,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[4,1,1,2,2,2,1] => [1,2,3,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[2,2,3,1,2,2,1] => [2,1,1,2,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[3,1,3,1,2,2,1] => [1,1,1,1,2,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[2,3,2,1,2,2,1] => [1,1,1,1,2,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[3,2,2,1,2,2,1] => [1,2,1,2,1] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[4,1,2,1,2,2,1] => [1,1,1,1,2,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[2,4,1,1,2,2,1] => [1,1,2,2,1] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[3,3,1,1,2,2,1] => [2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[4,2,1,1,2,2,1] => [1,1,2,2,1] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[5,1,1,1,2,2,1] => [1,3,2,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[2,2,2,3,1,2,1] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[3,1,2,3,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[2,3,1,3,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[3,2,1,3,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[4,1,1,3,1,2,1] => [1,2,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,2,3,2,1,2,1] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,1,3,2,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[2,3,2,2,1,2,1] => [1,1,2,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,2,2,1,2,1] => [1,3,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[4,1,2,2,1,2,1] => [1,1,2,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[2,4,1,2,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[3,3,1,2,1,2,1] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[4,2,1,2,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[5,1,1,2,1,2,1] => [1,2,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,2,4,1,1,2,1] => [2,1,2,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,1,4,1,1,2,1] => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[2,3,3,1,1,2,1] => [1,2,2,1,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[3,2,3,1,1,2,1] => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[4,1,3,1,1,2,1] => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[2,4,2,1,1,2,1] => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[3,3,2,1,1,2,1] => [2,1,2,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[4,2,2,1,1,2,1] => [1,2,2,1,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[5,1,2,1,1,2,1] => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[2,5,1,1,1,2,1] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[3,4,1,1,1,2,1] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[4,3,1,1,1,2,1] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[5,2,1,1,1,2,1] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[6,1,1,1,1,2,1] => [1,4,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[2,2,2,2,3,1,1] => [4,1,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[3,1,2,2,3,1,1] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[2,3,1,2,3,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[3,2,1,2,3,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[4,1,1,2,3,1,1] => [1,2,1,1,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[2,2,3,1,3,1,1] => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[3,1,3,1,3,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,3,2,1,3,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[3,2,2,1,3,1,1] => [1,2,1,1,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[4,1,2,1,3,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,4,1,1,3,1,1] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[3,3,1,1,3,1,1] => [2,2,1,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[4,2,1,1,3,1,1] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[5,1,1,1,3,1,1] => [1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[2,2,2,3,2,1,1] => [3,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[3,1,2,3,2,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,3,1,3,2,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[3,2,1,3,2,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[4,1,1,3,2,1,1] => [1,2,1,1,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[2,2,3,2,2,1,1] => [2,1,2,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[3,1,3,2,2,1,1] => [1,1,1,2,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[2,3,2,2,2,1,1] => [1,1,3,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[3,2,2,2,2,1,1] => [1,4,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[4,1,2,2,2,1,1] => [1,1,3,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[2,4,1,2,2,1,1] => [1,1,1,2,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[3,3,1,2,2,1,1] => [2,1,2,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[4,2,1,2,2,1,1] => [1,1,1,2,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[5,1,1,2,2,1,1] => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[2,2,4,1,2,1,1] => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[3,1,4,1,2,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,3,3,1,2,1,1] => [1,2,1,1,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[3,2,3,1,2,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[4,1,3,1,2,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,4,2,1,2,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[3,3,2,1,2,1,1] => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[4,2,2,1,2,1,1] => [1,2,1,1,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[5,1,2,1,2,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,5,1,1,2,1,1] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[3,4,1,1,2,1,1] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[4,3,1,1,2,1,1] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[5,2,1,1,2,1,1] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[6,1,1,1,2,1,1] => [1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[2,2,2,4,1,1,1] => [3,1,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[3,1,2,4,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[2,3,1,4,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[3,2,1,4,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[4,1,1,4,1,1,1] => [1,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,2,3,3,1,1,1] => [2,2,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[3,1,3,3,1,1,1] => [1,1,2,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[2,3,2,3,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[3,2,2,3,1,1,1] => [1,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[4,1,2,3,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[2,4,1,3,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[3,3,1,3,1,1,1] => [2,1,1,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[4,2,1,3,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[5,1,1,3,1,1,1] => [1,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,2,4,2,1,1,1] => [2,1,1,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[3,1,4,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[2,3,3,2,1,1,1] => [1,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[3,2,3,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[4,1,3,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[2,4,2,2,1,1,1] => [1,1,2,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[3,3,2,2,1,1,1] => [2,2,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[4,2,2,2,1,1,1] => [1,3,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[5,1,2,2,1,1,1] => [1,1,2,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[2,5,1,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[3,4,1,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[4,3,1,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[5,2,1,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[6,1,1,2,1,1,1] => [1,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,2,5,1,1,1,1] => [2,1,4] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[3,1,5,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[2,3,4,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[3,2,4,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[4,1,4,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[2,4,3,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[3,3,3,1,1,1,1] => [3,4] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 3
[4,2,3,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[5,1,3,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[2,5,2,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[3,4,2,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[4,3,2,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[5,2,2,1,1,1,1] => [1,2,4] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[6,1,2,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[2,6,1,1,1,1,1] => [1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[3,5,1,1,1,1,1] => [1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[4,4,1,1,1,1,1] => [2,5] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[5,3,1,1,1,1,1] => [1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[6,2,1,1,1,1,1] => [1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[7,1,1,1,1,1,1] => [1,6] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,2,2,4,2,1] => [1,2,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,2,4,2,2,1] => [1,1,1,2,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,2,5,2,2] => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,3,5,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,4,2,2,2,1] => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,5,2,2,2] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,5,3,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,5,2,2,1] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[2,6,2,2] => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[2,2,5,2,1] => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[6,2,2,2] => [1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[2,2,2,2,2,1,1] => [5,2] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[9,2] => [1,1] => [2] => [1,1,0,0] => 1
[1,9,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[10,2] => [1,1] => [2] => [1,1,0,0] => 1
[1,2,2,2,3,1,1] => [1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,2,2,3,1,2,1] => [1,2,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,2,4,1,1,1] => [1,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,2,3,1,2,2,1] => [1,1,1,1,2,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,2,3,1,3,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,2,3,2,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,2,4,1,1,2,1] => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,2,3,2,2,1,1] => [1,1,1,2,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,2,3,3,1,1,1] => [1,1,2,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,2,4,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,2,5,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,3,1,2,2,2,1] => [1,1,1,3,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,3,1,3,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,3,1,3,2,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,3,2,1,3,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,4,1,1,2,2,1] => [1,1,2,2,1] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,4,1,1,3,1,1] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[1,3,2,2,1,2,1] => [1,1,2,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,3,3,1,1,2,1] => [1,2,2,1,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,4,1,2,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,4,2,1,1,2,1] => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,5,1,1,1,2,1] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,3,2,3,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,3,3,1,2,1,1] => [1,2,1,1,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,3,4,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,4,1,2,2,1,1] => [1,1,1,2,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,4,1,3,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,5,1,1,2,1,1] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[1,4,2,2,1,1,1] => [1,1,2,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,4,3,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,5,2,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,6,1,1,1,1,1] => [1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[2,1,2,2,3,1,1] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[2,1,2,3,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[2,1,2,3,2,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,1,2,4,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[2,1,3,1,2,2,1] => [1,1,1,1,2,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[2,1,3,1,3,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,1,3,2,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[2,1,4,1,1,2,1] => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[2,1,3,2,2,1,1] => [1,1,1,2,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[2,1,3,3,1,1,1] => [1,1,2,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[2,1,4,1,2,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,1,4,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[2,1,5,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[2,2,1,2,3,1,1] => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,2,1,3,1,2,1] => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,2,1,3,2,1,1] => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,2,1,4,1,1,1] => [2,1,1,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[3,1,1,2,2,2,1] => [1,2,3,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[3,1,1,3,1,2,1] => [1,2,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[3,1,1,3,2,1,1] => [1,2,1,1,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[2,2,2,1,3,1,1] => [3,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[2,3,1,1,2,2,1] => [1,1,2,2,1] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[2,3,1,1,3,1,1] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[3,1,2,1,3,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[3,2,1,1,2,2,1] => [1,1,2,2,1] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[3,2,1,1,3,1,1] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[4,1,1,1,2,2,1] => [1,3,2,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[4,1,1,1,3,1,1] => [1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[2,2,3,1,1,2,1] => [2,1,2,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[2,3,1,2,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[2,3,2,1,1,2,1] => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[2,4,1,1,1,2,1] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[3,1,2,2,1,2,1] => [1,1,2,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[3,1,3,1,1,2,1] => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[3,2,1,2,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[4,1,1,2,1,2,1] => [1,2,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[3,2,2,1,1,2,1] => [1,2,2,1,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[3,3,1,1,1,2,1] => [2,3,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[4,1,2,1,1,2,1] => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[4,2,1,1,1,2,1] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[5,1,1,1,1,2,1] => [1,4,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[2,2,2,3,1,1,1] => [3,1,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,2,3,1,2,1,1] => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,2,3,2,1,1,1] => [2,1,1,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[2,2,4,1,1,1,1] => [2,1,4] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[2,3,1,2,2,1,1] => [1,1,1,2,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[2,3,1,3,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[2,3,2,1,2,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,4,1,1,2,1,1] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[2,3,2,2,1,1,1] => [1,1,2,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[2,3,3,1,1,1,1] => [1,2,4] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[2,4,1,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[2,4,2,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[2,5,1,1,1,1,1] => [1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[3,1,2,3,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[3,1,3,1,2,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[3,1,4,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[3,2,1,2,2,1,1] => [1,1,1,2,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[3,2,1,3,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[4,1,1,2,2,1,1] => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[4,1,1,3,1,1,1] => [1,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[3,3,1,1,2,1,1] => [2,2,1,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[4,1,2,1,2,1,1] => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[4,2,1,1,2,1,1] => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[5,1,1,1,2,1,1] => [1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[3,2,2,2,1,1,1] => [1,3,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[3,2,3,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[3,3,2,1,1,1,1] => [2,1,4] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[3,4,1,1,1,1,1] => [1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[4,1,2,2,1,1,1] => [1,1,2,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[4,1,3,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[4,2,1,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[4,2,2,1,1,1,1] => [1,2,4] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[4,3,1,1,1,1,1] => [1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[5,1,2,1,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[5,2,1,1,1,1,1] => [1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[6,1,1,1,1,1,1] => [1,6] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[11] => [1] => [1] => [1,0] => 1
[2,9] => [1,1] => [2] => [1,1,0,0] => 1
[1,1,2,2,4,1] => [2,2,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,3,1,3,1,3,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,3,1,2,3,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,3,1,2,1,4,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,3,1,1,1,5,1] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,2,3,2,1,3,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,2,3,1,3,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,2,3,1,1,4,1] => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,2,2,3,2,2,1] => [1,2,1,2,1] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,2,2,1,4,2,1] => [1,2,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,2,1,2,4,1] => [1,2,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,2,1,4,1,3,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,2,1,3,3,2,1] => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,2,1,3,1,4,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,2,1,2,1,5,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,2,1,1,5,2,1] => [1,1,2,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,2,1,1,3,4,1] => [1,1,2,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,2,1,1,1,6,1] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,5,1,3,1] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,4,3,2,1] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,4,1,4,1] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,3,1,5,1] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,2,5,2,1] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,2,3,4,1] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,2,1,6,1] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,7,1] => [5,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,2,3,2,3] => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,2,2,2,4] => [4,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,2,2,2,2,3] => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,2,2,3,4] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[2,2,3,5] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,2,3,2,4] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[2,3,2,5] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
[1,3,2,2,4] => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[5,1,1,1,1,2] => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,5,1] => [5,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,3,1,3,1] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,5,1,1,1] => [3,1,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,7,1] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,4,1,2,1] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,2,1,4,1] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,2,3,2,1] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,1,1,1,3,1] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,3,1,3,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,3,1,5,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,3,1,2,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,5,1,1,1,1,1] => [1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,5,1,3,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,7,1,1,1] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,6,1,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,4,1,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,4,1,4,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,4,1,1,1,2,1] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,4,3,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,1,2,1,3,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,2,1,4,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,2,1,6,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,1,3,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,2,1,1,1,4,1] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,2,1,1,3,2,1] => [1,1,2,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,2,3,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,2,3,4,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,3,1,1,2,1] => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,2,5,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,2,1,2,2,1] => [1,2,1,2,1] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,7,1,1,1] => [3,1,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,9,1] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,6,1,2,1] => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,1,5,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,3,1,7,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,3,1,4,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,5,1,1,1,3,1] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,5,1,3,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,5,1,5,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,5,1,2,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,7,1,1,1,1,1] => [1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,7,1,3,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,9,1,1,1] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,11,1] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,8,1,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,6,1,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,6,1,4,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,6,1,1,1,2,1] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,6,3,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,4,1,2,1,3,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,4,1,4,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,4,1,6,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,4,1,3,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,4,1,1,1,4,1] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,4,1,1,3,2,1] => [1,1,2,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,4,3,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,4,3,4,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,4,3,1,1,2,1] => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,4,5,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,4,2,1,2,2,1] => [1,1,1,1,2,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,2,1,6,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,2,1,8,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,1,5,1,2,1] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,2,3,4,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,2,3,6,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,3,3,1,2,1] => [1,1,2,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,2,5,2,1,1,1] => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,2,5,4,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,5,1,1,2,1] => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,2,7,2,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,4,1,2,2,1] => [1,1,1,1,2,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,9] => [2,1] => [1,2] => [1,0,1,1,0,0] => 1
[2,2,2,2,1,1,2] => [4,2,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,2,2,1,2,3] => [2,2,1,1,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,2,2,2,3] => [3,3,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[2,2,2,6] => [3,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[2,2,6,2] => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,6,4] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,5,5] => [1,2] => [2,1] => [1,1,0,0,1,0] => 1
[1,4,6] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,3,7] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,2,8] => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
[1,2,5,3,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,2,2,4,1] => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[2,2,2,5,1] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,2,3,5,1] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,2,2,5,2] => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,1,2,2,2,2,1] => [2,4,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,2,2,3,1,1] => [2,2,1,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,2,3,2,1,1] => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,3,2,2,1,1] => [2,1,2,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,2,2,2,2,1,1] => [1,4,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,2,2,2,4] => [2,3,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,2,5,1,1] => [2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,5,2,1,1] => [2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,4,2,2,1,1] => [1,1,2,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 3,0,1 6,1,0,1 15,0,0,0,1 27,3,1,0,0,1 61,2,0,0,0,0,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = 3\ q + q^{3}$
$F_{4} = 6\ q + q^{2} + q^{4}$
$F_{5} = 15\ q + q^{5}$
$F_{6} = 27\ q + 3\ q^{2} + q^{3} + q^{6}$
$F_{7} = 61\ q + 2\ q^{2} + q^{7}$
Description
The dominant dimension of the LNakayama algebra associated to a Dyck path.
To every Dyck path there is an LNakayama algebra associated as described in St000684The global dimension of the LNakayama algebra associated to a Dyck path..
To every Dyck path there is an LNakayama algebra associated as described in St000684The global dimension of the LNakayama algebra associated to a Dyck path..
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
delta morphism
Description
Apply the delta morphism to an integer composition.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
Map
complement
Description
The complement of a composition.
The complement of a composition $I$ is defined as follows:
If $I$ is the empty composition, then the complement is also the empty composition. Otherwise, let $S$ be the descent set corresponding to $I=(i_1,\dots,i_k)$, that is, the subset
$$\{ i_1, i_1 + i_2, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$$
of $\{ 1, 2, \ldots, |I|-1 \}$. Then, the complement of $I$ is the composition of the same size as $I$, whose descent set is $\{ 1, 2, \ldots, |I|-1 \} \setminus S$.
The complement of a composition $I$ coincides with the reversal (Mp00038reverse) of the composition conjugate (Mp00041conjugate) to $I$.
The complement of a composition $I$ is defined as follows:
If $I$ is the empty composition, then the complement is also the empty composition. Otherwise, let $S$ be the descent set corresponding to $I=(i_1,\dots,i_k)$, that is, the subset
$$\{ i_1, i_1 + i_2, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$$
of $\{ 1, 2, \ldots, |I|-1 \}$. Then, the complement of $I$ is the composition of the same size as $I$, whose descent set is $\{ 1, 2, \ldots, |I|-1 \} \setminus S$.
The complement of a composition $I$ coincides with the reversal (Mp00038reverse) of the composition conjugate (Mp00041conjugate) to $I$.
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