map length (tiers :: [[ Bag Nat3 ]])  =  [1,1,2,3,4,5,7,8,10,12,14,16,...]

length (list :: [ Bag Nat3 ])  =  Infinity

allUnique (list :: [ Bag Nat3 ])  =  True

ratioRepetitions (list :: [ Bag Nat3 ])  =  0 % 1

tiers :: [Bag Nat3]  =
  [ [Bag []]
  , [Bag [0]]
  , [ Bag [0,0]
    , Bag [1]
    ]
  , [ Bag [0,0,0]
    , Bag [0,1]
    , Bag [2]
    ]
  , [ Bag [0,0,0,0]
    , Bag [0,0,1]
    , Bag [0,2]
    , Bag [1,1]
    ]
  , [ Bag [0,0,0,0,0]
    , Bag [0,0,0,1]
    , Bag [0,0,2]
    , Bag [0,1,1]
    , Bag [1,2]
    ]
  , [ Bag [0,0,0,0,0,0]
    , Bag [0,0,0,0,1]
    , Bag [0,0,0,2]
    , Bag [0,0,1,1]
    , Bag [0,1,2]
    , Bag [1,1,1]
    , Bag [2,2]
    ]
  , [ Bag [0,0,0,0,0,0,0]
    , Bag [0,0,0,0,0,1]
    , Bag [0,0,0,0,2]
    , Bag [0,0,0,1,1]
    , Bag [0,0,1,2]
    , Bag [0,1,1,1]
    , Bag [0,2,2]
    , Bag [1,1,2]
    ]
  , [ Bag [0,0,0,0,0,0,0,0]
    , Bag [0,0,0,0,0,0,1]
    , Bag [0,0,0,0,0,2]
    , Bag [0,0,0,0,1,1]
    , Bag [0,0,0,1,2]
    , Bag [0,0,1,1,1]
    , Bag [0,0,2,2]
    , Bag [0,1,1,2]
    , Bag [1,1,1,1]
    , Bag [1,2,2]
    ]
  , [ Bag [0,0,0,0,0,0,0,0,0]
    , Bag [0,0,0,0,0,0,0,1]
    , Bag [0,0,0,0,0,0,2]
    , Bag [0,0,0,0,0,1,1]
    , Bag [0,0,0,0,1,2]
    , Bag [0,0,0,1,1,1]
    , Bag [0,0,0,2,2]
    , Bag [0,0,1,1,2]
    , Bag [0,1,1,1,1]
    , Bag [0,1,2,2]
    , Bag [1,1,1,2]
    , Bag [2,2,2]
    ]
  , [ Bag [0,0,0,0,0,0,0,0,0,0]
    , Bag [0,0,0,0,0,0,0,0,1]
    , Bag [0,0,0,0,0,0,0,2]
    , Bag [0,0,0,0,0,0,1,1]
    , Bag [0,0,0,0,0,1,2]
    , Bag [0,0,0,0,1,1,1]
    , Bag [0,0,0,0,2,2]
    , Bag [0,0,0,1,1,2]
    , Bag [0,0,1,1,1,1]
    , Bag [0,0,1,2,2]
    , Bag [0,1,1,1,2]
    , Bag [0,2,2,2]
    , Bag [1,1,1,1,1]
    , Bag [1,1,2,2]
    ]
  , [ Bag [0,0,0,0,0,0,0,0,0,0,0]
    , Bag [0,0,0,0,0,0,0,0,0,1]
    , Bag [0,0,0,0,0,0,0,0,2]
    , Bag [0,0,0,0,0,0,0,1,1]
    , Bag [0,0,0,0,0,0,1,2]
    , Bag [0,0,0,0,0,1,1,1]
    , Bag [0,0,0,0,0,2,2]
    , Bag [0,0,0,0,1,1,2]
    , Bag [0,0,0,1,1,1,1]
    , Bag [0,0,0,1,2,2]
    , Bag [0,0,1,1,1,2]
    , Bag [0,0,2,2,2]
    , Bag [0,1,1,1,1,1]
    , Bag [0,1,1,2,2]
    , Bag [1,1,1,1,2]
    , Bag [1,2,2,2]
    ]
  , ...
  ]