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