map length (tiers :: [[ Int->Int->Int->Int ]])  =  [1,1,7,25,...]

length (list :: [ Int->Int->Int->Int ])  =  Infinity

allUnique (list :: [ Int->Int->Int->Int ])  =  True

ratioRepetitions (list :: [ Int->Int->Int->Int ])  =  0 % 1

tiers :: [Int->Int->Int->Int]  =
  [ [\_ _ _ -> 0]
  , [\_ _ _ -> 1]
  , [ \x _ _ -> case x of
                0 -> 1
                _ -> 0
    , \x _ _ -> case x of
                0 -> 0
                _ -> 1
    , \_ y _ -> case y of
                0 -> 1
                _ -> 0
    , \_ y _ -> case y of
                0 -> 0
                _ -> 1
    , \_ _ z -> case z of
                0 -> 1
                _ -> 0
    , \_ _ z -> case z of
                0 -> 0
                _ -> 1
    , \_ _ _ -> -1
    ]
  , [ \x y _ -> case (x,y) of
                (0,0) -> 1
                _ -> 0
    , \x y _ -> case (x,y) of
                (_,0) -> 0
                (0,_) -> 1
                _ -> 0
    , \x _ z -> case (x,z) of
                (0,0) -> 1
                _ -> 0
    , \x _ z -> case (x,z) of
                (_,0) -> 0
                (0,_) -> 1
                _ -> 0
    , \x _ _ -> case x of
                0 -> -1
                _ -> 0
    , \x _ _ -> case x of
                1 -> 1
                _ -> 0
    , \x _ _ -> case x of
                1 -> 0
                _ -> 1
    , \x y _ -> case (x,y) of
                (0,_) -> 0
                (_,0) -> 1
                _ -> 0
    , \x y _ -> case (x,y) of
                (0,_) -> 0
                (_,0) -> 0
                _ -> 1
    , \x _ z -> case (x,z) of
                (0,_) -> 0
                (_,0) -> 1
                _ -> 0
    , \x _ z -> case (x,z) of
                (0,_) -> 0
                (_,0) -> 0
                _ -> 1
    , \x _ _ -> case x of
                0 -> 0
                _ -> -1
    , \_ y z -> case (y,z) of
                (0,0) -> 1
                _ -> 0
    , \_ y z -> case (y,z) of
                (_,0) -> 0
                (0,_) -> 1
                _ -> 0
    , \_ y _ -> case y of
                0 -> -1
                _ -> 0
    , \_ y _ -> case y of
                1 -> 1
                _ -> 0
    , \_ y _ -> case y of
                1 -> 0
                _ -> 1
    , \_ y z -> case (y,z) of
                (0,_) -> 0
                (_,0) -> 1
                _ -> 0
    , \_ y z -> case (y,z) of
                (0,_) -> 0
                (_,0) -> 0
                _ -> 1
    , \_ y _ -> case y of
                0 -> 0
                _ -> -1
    , \_ _ z -> case z of
                0 -> -1
                _ -> 0
    , \_ _ z -> case z of
                1 -> 1
                _ -> 0
    , \_ _ z -> case z of
                1 -> 0
                _ -> 1
    , \_ _ z -> case z of
                0 -> 0
                _ -> -1
    , \_ _ _ -> 2
    ]
  , ...
  ]