map length (tiers :: [[ Map Nat3 Nat3 ]])  =  [1,1,2,4,5,7,8,9,9,8,6,3,...]

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

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

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

tiers :: [Map Nat3 Nat3]  =
  [ [Map []]
  , [Map [(0,0)]]
  , [ Map [(0,1)]
    , Map [(1,0)]
    ]
  , [ Map [(0,2)]
    , Map [(1,1)]
    , Map [(0,0),(1,0)]
    , Map [(2,0)]
    ]
  , [ Map [(1,2)]
    , Map [(0,0),(1,1)]
    , Map [(0,1),(1,0)]
    , Map [(2,1)]
    , Map [(0,0),(2,0)]
    ]
  , [ Map [(0,0),(1,2)]
    , Map [(0,1),(1,1)]
    , Map [(0,2),(1,0)]
    , Map [(2,2)]
    , Map [(0,0),(2,1)]
    , Map [(0,1),(2,0)]
    , Map [(1,0),(2,0)]
    ]
  , [ Map [(0,1),(1,2)]
    , Map [(0,2),(1,1)]
    , Map [(0,0),(2,2)]
    , Map [(0,1),(2,1)]
    , Map [(0,2),(2,0)]
    , Map [(1,0),(2,1)]
    , Map [(1,1),(2,0)]
    , Map [(0,0),(1,0),(2,0)]
    ]
  , [ Map [(0,2),(1,2)]
    , Map [(0,1),(2,2)]
    , Map [(0,2),(2,1)]
    , Map [(1,0),(2,2)]
    , Map [(1,1),(2,1)]
    , Map [(1,2),(2,0)]
    , Map [(0,0),(1,0),(2,1)]
    , Map [(0,0),(1,1),(2,0)]
    , Map [(0,1),(1,0),(2,0)]
    ]
  , [ Map [(0,2),(2,2)]
    , Map [(1,1),(2,2)]
    , Map [(1,2),(2,1)]
    , Map [(0,0),(1,0),(2,2)]
    , Map [(0,0),(1,1),(2,1)]
    , Map [(0,0),(1,2),(2,0)]
    , Map [(0,1),(1,0),(2,1)]
    , Map [(0,1),(1,1),(2,0)]
    , Map [(0,2),(1,0),(2,0)]
    ]
  , [ Map [(1,2),(2,2)]
    , Map [(0,0),(1,1),(2,2)]
    , Map [(0,0),(1,2),(2,1)]
    , Map [(0,1),(1,0),(2,2)]
    , Map [(0,1),(1,1),(2,1)]
    , Map [(0,1),(1,2),(2,0)]
    , Map [(0,2),(1,0),(2,1)]
    , Map [(0,2),(1,1),(2,0)]
    ]
  , [ Map [(0,0),(1,2),(2,2)]
    , Map [(0,1),(1,1),(2,2)]
    , Map [(0,1),(1,2),(2,1)]
    , Map [(0,2),(1,0),(2,2)]
    , Map [(0,2),(1,1),(2,1)]
    , Map [(0,2),(1,2),(2,0)]
    ]
  , [ Map [(0,1),(1,2),(2,2)]
    , Map [(0,2),(1,1),(2,2)]
    , Map [(0,2),(1,2),(2,1)]
    ]
  , ...
  ]