map length (tiers :: [[ Bag () ]])  =  [1,1,1,1,1,1,1,1,1,1,1,1,...]

length (list :: [ Bag () ])  =  Infinity

allUnique (list :: [ Bag () ])  =  True

ratioRepetitions (list :: [ Bag () ])  =  0 % 1

tiers :: [Bag ()]  =
  [ [Bag []]
  , [Bag [()]]
  , [Bag [(),()]]
  , [Bag [(),(),()]]
  , [Bag [(),(),(),()]]
  , [Bag [(),(),(),(),()]]
  , [Bag [(),(),(),(),(),()]]
  , [Bag [(),(),(),(),(),(),()]]
  , [Bag [(),(),(),(),(),(),(),()]]
  , [Bag [(),(),(),(),(),(),(),(),()]]
  , [Bag [(),(),(),(),(),(),(),(),(),()]]
  , [Bag [(),(),(),(),(),(),(),(),(),(),()]]
  , ...
  ]