map length (tiers :: [[ Map Nat Nat ]])  =  [1,1,2,4,7,12,20,33,53,84,131,202,...]

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

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

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

tiers :: [Map Nat Nat]  =
  [ [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 [(0,3)]
    , Map [(1,2)]
    , Map [(0,0),(1,1)]
    , Map [(0,1),(1,0)]
    , Map [(2,1)]
    , Map [(0,0),(2,0)]
    , Map [(3,0)]
    ]
  , [ Map [(0,4)]
    , Map [(1,3)]
    , 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 [(3,1)]
    , Map [(0,0),(3,0)]
    , Map [(1,0),(2,0)]
    , Map [(4,0)]
    ]
  , [ Map [(0,5)]
    , Map [(1,4)]
    , Map [(0,0),(1,3)]
    , Map [(0,1),(1,2)]
    , Map [(0,2),(1,1)]
    , Map [(0,3),(1,0)]
    , Map [(2,3)]
    , Map [(0,0),(2,2)]
    , Map [(0,1),(2,1)]
    , Map [(0,2),(2,0)]
    , Map [(3,2)]
    , Map [(0,0),(3,1)]
    , Map [(0,1),(3,0)]
    , Map [(1,0),(2,1)]
    , Map [(1,1),(2,0)]
    , Map [(4,1)]
    , Map [(0,0),(1,0),(2,0)]
    , Map [(0,0),(4,0)]
    , Map [(1,0),(3,0)]
    , Map [(5,0)]
    ]
  , [ Map [(0,6)]
    , Map [(1,5)]
    , Map [(0,0),(1,4)]
    , Map [(0,1),(1,3)]
    , Map [(0,2),(1,2)]
    , Map [(0,3),(1,1)]
    , Map [(0,4),(1,0)]
    , Map [(2,4)]
    , Map [(0,0),(2,3)]
    , Map [(0,1),(2,2)]
    , Map [(0,2),(2,1)]
    , Map [(0,3),(2,0)]
    , Map [(3,3)]
    , Map [(0,0),(3,2)]
    , Map [(0,1),(3,1)]
    , Map [(0,2),(3,0)]
    , Map [(1,0),(2,2)]
    , Map [(1,1),(2,1)]
    , Map [(1,2),(2,0)]
    , Map [(4,2)]
    , Map [(0,0),(1,0),(2,1)]
    , Map [(0,0),(1,1),(2,0)]
    , Map [(0,1),(1,0),(2,0)]
    , Map [(0,0),(4,1)]
    , Map [(0,1),(4,0)]
    , Map [(1,0),(3,1)]
    , Map [(1,1),(3,0)]
    , Map [(5,1)]
    , Map [(0,0),(1,0),(3,0)]
    , Map [(0,0),(5,0)]
    , Map [(1,0),(4,0)]
    , Map [(2,0),(3,0)]
    , Map [(6,0)]
    ]
  , [ Map [(0,7)]
    , Map [(1,6)]
    , Map [(0,0),(1,5)]
    , Map [(0,1),(1,4)]
    , Map [(0,2),(1,3)]
    , Map [(0,3),(1,2)]
    , Map [(0,4),(1,1)]
    , Map [(0,5),(1,0)]
    , Map [(2,5)]
    , Map [(0,0),(2,4)]
    , Map [(0,1),(2,3)]
    , Map [(0,2),(2,2)]
    , Map [(0,3),(2,1)]
    , Map [(0,4),(2,0)]
    , Map [(3,4)]
    , Map [(0,0),(3,3)]
    , Map [(0,1),(3,2)]
    , Map [(0,2),(3,1)]
    , Map [(0,3),(3,0)]
    , Map [(1,0),(2,3)]
    , Map [(1,1),(2,2)]
    , Map [(1,2),(2,1)]
    , Map [(1,3),(2,0)]
    , Map [(4,3)]
    , 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 [(0,0),(4,2)]
    , Map [(0,1),(4,1)]
    , Map [(0,2),(4,0)]
    , Map [(1,0),(3,2)]
    , Map [(1,1),(3,1)]
    , Map [(1,2),(3,0)]
    , Map [(5,2)]
    , Map [(0,0),(1,0),(3,1)]
    , Map [(0,0),(1,1),(3,0)]
    , Map [(0,1),(1,0),(3,0)]
    , Map [(0,0),(5,1)]
    , Map [(0,1),(5,0)]
    , Map [(1,0),(4,1)]
    , Map [(1,1),(4,0)]
    , Map [(2,0),(3,1)]
    , Map [(2,1),(3,0)]
    , Map [(6,1)]
    , Map [(0,0),(1,0),(4,0)]
    , Map [(0,0),(2,0),(3,0)]
    , Map [(0,0),(6,0)]
    , Map [(1,0),(5,0)]
    , Map [(2,0),(4,0)]
    , Map [(7,0)]
    ]
  , [ Map [(0,8)]
    , Map [(1,7)]
    , Map [(0,0),(1,6)]
    , Map [(0,1),(1,5)]
    , Map [(0,2),(1,4)]
    , Map [(0,3),(1,3)]
    , Map [(0,4),(1,2)]
    , Map [(0,5),(1,1)]
    , Map [(0,6),(1,0)]
    , Map [(2,6)]
    , Map [(0,0),(2,5)]
    , Map [(0,1),(2,4)]
    , Map [(0,2),(2,3)]
    , Map [(0,3),(2,2)]
    , Map [(0,4),(2,1)]
    , Map [(0,5),(2,0)]
    , Map [(3,5)]
    , Map [(0,0),(3,4)]
    , Map [(0,1),(3,3)]
    , Map [(0,2),(3,2)]
    , Map [(0,3),(3,1)]
    , Map [(0,4),(3,0)]
    , Map [(1,0),(2,4)]
    , Map [(1,1),(2,3)]
    , Map [(1,2),(2,2)]
    , Map [(1,3),(2,1)]
    , Map [(1,4),(2,0)]
    , Map [(4,4)]
    , Map [(0,0),(1,0),(2,3)]
    , Map [(0,0),(1,1),(2,2)]
    , Map [(0,0),(1,2),(2,1)]
    , Map [(0,0),(1,3),(2,0)]
    , 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 [(0,3),(1,0),(2,0)]
    , Map [(0,0),(4,3)]
    , Map [(0,1),(4,2)]
    , Map [(0,2),(4,1)]
    , Map [(0,3),(4,0)]
    , Map [(1,0),(3,3)]
    , Map [(1,1),(3,2)]
    , Map [(1,2),(3,1)]
    , Map [(1,3),(3,0)]
    , Map [(5,3)]
    , Map [(0,0),(1,0),(3,2)]
    , Map [(0,0),(1,1),(3,1)]
    , Map [(0,0),(1,2),(3,0)]
    , Map [(0,1),(1,0),(3,1)]
    , Map [(0,1),(1,1),(3,0)]
    , Map [(0,2),(1,0),(3,0)]
    , Map [(0,0),(5,2)]
    , Map [(0,1),(5,1)]
    , Map [(0,2),(5,0)]
    , Map [(1,0),(4,2)]
    , Map [(1,1),(4,1)]
    , Map [(1,2),(4,0)]
    , Map [(2,0),(3,2)]
    , Map [(2,1),(3,1)]
    , Map [(2,2),(3,0)]
    , Map [(6,2)]
    , Map [(0,0),(1,0),(4,1)]
    , Map [(0,0),(1,1),(4,0)]
    , Map [(0,1),(1,0),(4,0)]
    , Map [(0,0),(2,0),(3,1)]
    , Map [(0,0),(2,1),(3,0)]
    , Map [(0,1),(2,0),(3,0)]
    , Map [(0,0),(6,1)]
    , Map [(0,1),(6,0)]
    , Map [(1,0),(5,1)]
    , Map [(1,1),(5,0)]
    , Map [(2,0),(4,1)]
    , Map [(2,1),(4,0)]
    , Map [(7,1)]
    , Map [(0,0),(1,0),(5,0)]
    , Map [(0,0),(2,0),(4,0)]
    , Map [(0,0),(7,0)]
    , Map [(1,0),(2,0),(3,0)]
    , Map [(1,0),(6,0)]
    , Map [(2,0),(5,0)]
    , Map [(3,0),(4,0)]
    , Map [(8,0)]
    ]
  , [ Map [(0,9)]
    , Map [(1,8)]
    , Map [(0,0),(1,7)]
    , Map [(0,1),(1,6)]
    , Map [(0,2),(1,5)]
    , Map [(0,3),(1,4)]
    , Map [(0,4),(1,3)]
    , Map [(0,5),(1,2)]
    , Map [(0,6),(1,1)]
    , Map [(0,7),(1,0)]
    , Map [(2,7)]
    , Map [(0,0),(2,6)]
    , Map [(0,1),(2,5)]
    , Map [(0,2),(2,4)]
    , Map [(0,3),(2,3)]
    , Map [(0,4),(2,2)]
    , Map [(0,5),(2,1)]
    , Map [(0,6),(2,0)]
    , Map [(3,6)]
    , Map [(0,0),(3,5)]
    , Map [(0,1),(3,4)]
    , Map [(0,2),(3,3)]
    , Map [(0,3),(3,2)]
    , Map [(0,4),(3,1)]
    , Map [(0,5),(3,0)]
    , Map [(1,0),(2,5)]
    , Map [(1,1),(2,4)]
    , Map [(1,2),(2,3)]
    , Map [(1,3),(2,2)]
    , Map [(1,4),(2,1)]
    , Map [(1,5),(2,0)]
    , Map [(4,5)]
    , Map [(0,0),(1,0),(2,4)]
    , Map [(0,0),(1,1),(2,3)]
    , Map [(0,0),(1,2),(2,2)]
    , Map [(0,0),(1,3),(2,1)]
    , Map [(0,0),(1,4),(2,0)]
    , Map [(0,1),(1,0),(2,3)]
    , Map [(0,1),(1,1),(2,2)]
    , Map [(0,1),(1,2),(2,1)]
    , Map [(0,1),(1,3),(2,0)]
    , Map [(0,2),(1,0),(2,2)]
    , Map [(0,2),(1,1),(2,1)]
    , Map [(0,2),(1,2),(2,0)]
    , Map [(0,3),(1,0),(2,1)]
    , Map [(0,3),(1,1),(2,0)]
    , Map [(0,4),(1,0),(2,0)]
    , Map [(0,0),(4,4)]
    , Map [(0,1),(4,3)]
    , Map [(0,2),(4,2)]
    , Map [(0,3),(4,1)]
    , Map [(0,4),(4,0)]
    , Map [(1,0),(3,4)]
    , Map [(1,1),(3,3)]
    , Map [(1,2),(3,2)]
    , Map [(1,3),(3,1)]
    , Map [(1,4),(3,0)]
    , Map [(5,4)]
    , Map [(0,0),(1,0),(3,3)]
    , Map [(0,0),(1,1),(3,2)]
    , Map [(0,0),(1,2),(3,1)]
    , Map [(0,0),(1,3),(3,0)]
    , Map [(0,1),(1,0),(3,2)]
    , Map [(0,1),(1,1),(3,1)]
    , Map [(0,1),(1,2),(3,0)]
    , Map [(0,2),(1,0),(3,1)]
    , Map [(0,2),(1,1),(3,0)]
    , Map [(0,3),(1,0),(3,0)]
    , Map [(0,0),(5,3)]
    , Map [(0,1),(5,2)]
    , Map [(0,2),(5,1)]
    , Map [(0,3),(5,0)]
    , Map [(1,0),(4,3)]
    , Map [(1,1),(4,2)]
    , Map [(1,2),(4,1)]
    , Map [(1,3),(4,0)]
    , Map [(2,0),(3,3)]
    , Map [(2,1),(3,2)]
    , Map [(2,2),(3,1)]
    , Map [(2,3),(3,0)]
    , Map [(6,3)]
    , Map [(0,0),(1,0),(4,2)]
    , Map [(0,0),(1,1),(4,1)]
    , Map [(0,0),(1,2),(4,0)]
    , Map [(0,1),(1,0),(4,1)]
    , Map [(0,1),(1,1),(4,0)]
    , Map [(0,2),(1,0),(4,0)]
    , Map [(0,0),(2,0),(3,2)]
    , Map [(0,0),(2,1),(3,1)]
    , Map [(0,0),(2,2),(3,0)]
    , Map [(0,1),(2,0),(3,1)]
    , Map [(0,1),(2,1),(3,0)]
    , Map [(0,2),(2,0),(3,0)]
    , Map [(0,0),(6,2)]
    , Map [(0,1),(6,1)]
    , Map [(0,2),(6,0)]
    , Map [(1,0),(5,2)]
    , Map [(1,1),(5,1)]
    , Map [(1,2),(5,0)]
    , Map [(2,0),(4,2)]
    , Map [(2,1),(4,1)]
    , Map [(2,2),(4,0)]
    , Map [(7,2)]
    , Map [(0,0),(1,0),(5,1)]
    , Map [(0,0),(1,1),(5,0)]
    , Map [(0,1),(1,0),(5,0)]
    , Map [(0,0),(2,0),(4,1)]
    , Map [(0,0),(2,1),(4,0)]
    , Map [(0,1),(2,0),(4,0)]
    , Map [(0,0),(7,1)]
    , Map [(0,1),(7,0)]
    , Map [(1,0),(2,0),(3,1)]
    , Map [(1,0),(2,1),(3,0)]
    , Map [(1,1),(2,0),(3,0)]
    , Map [(1,0),(6,1)]
    , Map [(1,1),(6,0)]
    , Map [(2,0),(5,1)]
    , Map [(2,1),(5,0)]
    , Map [(3,0),(4,1)]
    , Map [(3,1),(4,0)]
    , Map [(8,1)]
    , Map [(0,0),(1,0),(2,0),(3,0)]
    , Map [(0,0),(1,0),(6,0)]
    , Map [(0,0),(2,0),(5,0)]
    , Map [(0,0),(3,0),(4,0)]
    , Map [(0,0),(8,0)]
    , Map [(1,0),(2,0),(4,0)]
    , Map [(1,0),(7,0)]
    , Map [(2,0),(6,0)]
    , Map [(3,0),(5,0)]
    , Map [(9,0)]
    ]
  , [ Map [(0,10)]
    , Map [(1,9)]
    , Map [(0,0),(1,8)]
    , Map [(0,1),(1,7)]
    , Map [(0,2),(1,6)]
    , Map [(0,3),(1,5)]
    , Map [(0,4),(1,4)]
    , Map [(0,5),(1,3)]
    , Map [(0,6),(1,2)]
    , Map [(0,7),(1,1)]
    , Map [(0,8),(1,0)]
    , Map [(2,8)]
    , Map [(0,0),(2,7)]
    , Map [(0,1),(2,6)]
    , Map [(0,2),(2,5)]
    , Map [(0,3),(2,4)]
    , Map [(0,4),(2,3)]
    , Map [(0,5),(2,2)]
    , Map [(0,6),(2,1)]
    , Map [(0,7),(2,0)]
    , Map [(3,7)]
    , Map [(0,0),(3,6)]
    , Map [(0,1),(3,5)]
    , Map [(0,2),(3,4)]
    , Map [(0,3),(3,3)]
    , Map [(0,4),(3,2)]
    , Map [(0,5),(3,1)]
    , Map [(0,6),(3,0)]
    , Map [(1,0),(2,6)]
    , Map [(1,1),(2,5)]
    , Map [(1,2),(2,4)]
    , Map [(1,3),(2,3)]
    , Map [(1,4),(2,2)]
    , Map [(1,5),(2,1)]
    , Map [(1,6),(2,0)]
    , Map [(4,6)]
    , Map [(0,0),(1,0),(2,5)]
    , Map [(0,0),(1,1),(2,4)]
    , Map [(0,0),(1,2),(2,3)]
    , Map [(0,0),(1,3),(2,2)]
    , Map [(0,0),(1,4),(2,1)]
    , Map [(0,0),(1,5),(2,0)]
    , Map [(0,1),(1,0),(2,4)]
    , Map [(0,1),(1,1),(2,3)]
    , Map [(0,1),(1,2),(2,2)]
    , Map [(0,1),(1,3),(2,1)]
    , Map [(0,1),(1,4),(2,0)]
    , Map [(0,2),(1,0),(2,3)]
    , Map [(0,2),(1,1),(2,2)]
    , Map [(0,2),(1,2),(2,1)]
    , Map [(0,2),(1,3),(2,0)]
    , Map [(0,3),(1,0),(2,2)]
    , Map [(0,3),(1,1),(2,1)]
    , Map [(0,3),(1,2),(2,0)]
    , Map [(0,4),(1,0),(2,1)]
    , Map [(0,4),(1,1),(2,0)]
    , Map [(0,5),(1,0),(2,0)]
    , Map [(0,0),(4,5)]
    , Map [(0,1),(4,4)]
    , Map [(0,2),(4,3)]
    , Map [(0,3),(4,2)]
    , Map [(0,4),(4,1)]
    , Map [(0,5),(4,0)]
    , Map [(1,0),(3,5)]
    , Map [(1,1),(3,4)]
    , Map [(1,2),(3,3)]
    , Map [(1,3),(3,2)]
    , Map [(1,4),(3,1)]
    , Map [(1,5),(3,0)]
    , Map [(5,5)]
    , Map [(0,0),(1,0),(3,4)]
    , Map [(0,0),(1,1),(3,3)]
    , Map [(0,0),(1,2),(3,2)]
    , Map [(0,0),(1,3),(3,1)]
    , Map [(0,0),(1,4),(3,0)]
    , Map [(0,1),(1,0),(3,3)]
    , Map [(0,1),(1,1),(3,2)]
    , Map [(0,1),(1,2),(3,1)]
    , Map [(0,1),(1,3),(3,0)]
    , Map [(0,2),(1,0),(3,2)]
    , Map [(0,2),(1,1),(3,1)]
    , Map [(0,2),(1,2),(3,0)]
    , Map [(0,3),(1,0),(3,1)]
    , Map [(0,3),(1,1),(3,0)]
    , Map [(0,4),(1,0),(3,0)]
    , Map [(0,0),(5,4)]
    , Map [(0,1),(5,3)]
    , Map [(0,2),(5,2)]
    , Map [(0,3),(5,1)]
    , Map [(0,4),(5,0)]
    , Map [(1,0),(4,4)]
    , Map [(1,1),(4,3)]
    , Map [(1,2),(4,2)]
    , Map [(1,3),(4,1)]
    , Map [(1,4),(4,0)]
    , Map [(2,0),(3,4)]
    , Map [(2,1),(3,3)]
    , Map [(2,2),(3,2)]
    , Map [(2,3),(3,1)]
    , Map [(2,4),(3,0)]
    , Map [(6,4)]
    , Map [(0,0),(1,0),(4,3)]
    , Map [(0,0),(1,1),(4,2)]
    , Map [(0,0),(1,2),(4,1)]
    , Map [(0,0),(1,3),(4,0)]
    , Map [(0,1),(1,0),(4,2)]
    , Map [(0,1),(1,1),(4,1)]
    , Map [(0,1),(1,2),(4,0)]
    , Map [(0,2),(1,0),(4,1)]
    , Map [(0,2),(1,1),(4,0)]
    , Map [(0,3),(1,0),(4,0)]
    , Map [(0,0),(2,0),(3,3)]
    , Map [(0,0),(2,1),(3,2)]
    , Map [(0,0),(2,2),(3,1)]
    , Map [(0,0),(2,3),(3,0)]
    , Map [(0,1),(2,0),(3,2)]
    , Map [(0,1),(2,1),(3,1)]
    , Map [(0,1),(2,2),(3,0)]
    , Map [(0,2),(2,0),(3,1)]
    , Map [(0,2),(2,1),(3,0)]
    , Map [(0,3),(2,0),(3,0)]
    , Map [(0,0),(6,3)]
    , Map [(0,1),(6,2)]
    , Map [(0,2),(6,1)]
    , Map [(0,3),(6,0)]
    , Map [(1,0),(5,3)]
    , Map [(1,1),(5,2)]
    , Map [(1,2),(5,1)]
    , Map [(1,3),(5,0)]
    , Map [(2,0),(4,3)]
    , Map [(2,1),(4,2)]
    , Map [(2,2),(4,1)]
    , Map [(2,3),(4,0)]
    , Map [(7,3)]
    , Map [(0,0),(1,0),(5,2)]
    , Map [(0,0),(1,1),(5,1)]
    , Map [(0,0),(1,2),(5,0)]
    , Map [(0,1),(1,0),(5,1)]
    , Map [(0,1),(1,1),(5,0)]
    , Map [(0,2),(1,0),(5,0)]
    , Map [(0,0),(2,0),(4,2)]
    , Map [(0,0),(2,1),(4,1)]
    , Map [(0,0),(2,2),(4,0)]
    , Map [(0,1),(2,0),(4,1)]
    , Map [(0,1),(2,1),(4,0)]
    , Map [(0,2),(2,0),(4,0)]
    , Map [(0,0),(7,2)]
    , Map [(0,1),(7,1)]
    , Map [(0,2),(7,0)]
    , Map [(1,0),(2,0),(3,2)]
    , Map [(1,0),(2,1),(3,1)]
    , Map [(1,0),(2,2),(3,0)]
    , Map [(1,1),(2,0),(3,1)]
    , Map [(1,1),(2,1),(3,0)]
    , Map [(1,2),(2,0),(3,0)]
    , Map [(1,0),(6,2)]
    , Map [(1,1),(6,1)]
    , Map [(1,2),(6,0)]
    , Map [(2,0),(5,2)]
    , Map [(2,1),(5,1)]
    , Map [(2,2),(5,0)]
    , Map [(3,0),(4,2)]
    , Map [(3,1),(4,1)]
    , Map [(3,2),(4,0)]
    , Map [(8,2)]
    , Map [(0,0),(1,0),(2,0),(3,1)]
    , Map [(0,0),(1,0),(2,1),(3,0)]
    , Map [(0,0),(1,1),(2,0),(3,0)]
    , Map [(0,1),(1,0),(2,0),(3,0)]
    , Map [(0,0),(1,0),(6,1)]
    , Map [(0,0),(1,1),(6,0)]
    , Map [(0,1),(1,0),(6,0)]
    , Map [(0,0),(2,0),(5,1)]
    , Map [(0,0),(2,1),(5,0)]
    , Map [(0,1),(2,0),(5,0)]
    , Map [(0,0),(3,0),(4,1)]
    , Map [(0,0),(3,1),(4,0)]
    , Map [(0,1),(3,0),(4,0)]
    , Map [(0,0),(8,1)]
    , Map [(0,1),(8,0)]
    , Map [(1,0),(2,0),(4,1)]
    , Map [(1,0),(2,1),(4,0)]
    , Map [(1,1),(2,0),(4,0)]
    , Map [(1,0),(7,1)]
    , Map [(1,1),(7,0)]
    , Map [(2,0),(6,1)]
    , Map [(2,1),(6,0)]
    , Map [(3,0),(5,1)]
    , Map [(3,1),(5,0)]
    , Map [(9,1)]
    , Map [(0,0),(1,0),(2,0),(4,0)]
    , Map [(0,0),(1,0),(7,0)]
    , Map [(0,0),(2,0),(6,0)]
    , Map [(0,0),(3,0),(5,0)]
    , Map [(0,0),(9,0)]
    , Map [(1,0),(2,0),(5,0)]
    , Map [(1,0),(3,0),(4,0)]
    , Map [(1,0),(8,0)]
    , Map [(2,0),(7,0)]
    , Map [(3,0),(6,0)]
    , Map [(4,0),(5,0)]
    , Map [(10,0)]
    ]
  , ...
  ]
