O  -> Class 0
  O O -> Class 1
    O -> Class 1
  O O -> Class 2
    O -> Class 1
  O O -> Class 2
    O -> Class 1
 OO O -> Class 3
 OO   -> Class 3
 OO O -> Class 4
 OO   -> Class 3
OOO   -> Class 5
OO    -> Class 5
O     -> Class 5
OO    -> Class 6
OOO   -> Class 7
OOOO  -> Class 8
OOOOO -> Class 9
O     -> Class 5
 O    -> Class 3
  O   -> Class 2
   O  -> Class 0
    O -> Class 1
  O O -> Class 4
 OO O -> Class 9
 OO   -> Class 7
OOO   -> Class 8
OO    -> Class 6
OOOO  -> new Input and all Classes exhausted
OOOOO -> new Input and all Classes exhausted