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

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

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

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

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