map length (tiers :: [[ Int->Int ]])  =  [1,1,3,5,10,16,30,48,80,...]

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

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

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

tiers :: [Int->Int]  =
  [ [\_ -> 0]
  , [\_ -> 1]
  , [ \x -> case x of
            0 -> 1
            _ -> 0
    , \x -> case x of
            0 -> 0
            _ -> 1
    , \_ -> -1
    ]
  , [ \x -> case x of
            0 -> -1
            _ -> 0
    , \x -> case x of
            1 -> 1
            _ -> 0
    , \x -> case x of
            1 -> 0
            _ -> 1
    , \x -> case x of
            0 -> 0
            _ -> -1
    , \_ -> 2
    ]
  , [ \x -> case x of
            0 -> 2
            _ -> 0
    , \x -> case x of
            1 -> -1
            _ -> 0
    , \x -> case x of
            -1 -> 1
            _ -> 0
    , \x -> case x of
            0 -> -1
            _ -> 1
    , \x -> case x of
            0 -> 0
            1 -> 0
            _ -> 1
    , \x -> case x of
            -1 -> 0
            _ -> 1
    , \x -> case x of
            0 -> 1
            _ -> -1
    , \x -> case x of
            1 -> 0
            _ -> -1
    , \x -> case x of
            0 -> 0
            _ -> 2
    , \_ -> -2
    ]
  , [ \x -> case x of
            0 -> -2
            _ -> 0
    , \x -> case x of
            1 -> 2
            _ -> 0
    , \x -> case x of
            0 -> 1
            1 -> 1
            _ -> 0
    , \x -> case x of
            -1 -> -1
            _ -> 0
    , \x -> case x of
            2 -> 1
            _ -> 0
    , \x -> case x of
            0 -> 2
            _ -> 1
    , \x -> case x of
            1 -> -1
            _ -> 1
    , \x -> case x of
            0 -> 0
            -1 -> 0
            _ -> 1
    , \x -> case x of
            2 -> 0
            _ -> 1
    , \x -> case x of
            1 -> 1
            _ -> -1
    , \x -> case x of
            0 -> 0
            1 -> 0
            _ -> -1
    , \x -> case x of
            -1 -> 0
            _ -> -1
    , \x -> case x of
            0 -> 1
            _ -> 2
    , \x -> case x of
            1 -> 0
            _ -> 2
    , \x -> case x of
            0 -> 0
            _ -> -2
    , \_ -> 3
    ]
  , [ \x -> case x of
            0 -> 3
            _ -> 0
    , \x -> case x of
            1 -> -2
            _ -> 0
    , \x -> case x of
            0 -> 1
            1 -> -1
            _ -> 0
    , \x -> case x of
            0 -> -1
            1 -> 1
            _ -> 0
    , \x -> case x of
            -1 -> 2
            _ -> 0
    , \x -> case x of
            0 -> 1
            -1 -> 1
            _ -> 0
    , \x -> case x of
            2 -> -1
            _ -> 0
    , \x -> case x of
            -2 -> 1
            _ -> 0
    , \x -> case x of
            0 -> -2
            _ -> 1
    , \x -> case x of
            1 -> 2
            _ -> 1
    , \x -> case x of
            0 -> 0
            1 -> -1
            _ -> 1
    , \x -> case x of
            0 -> -1
            1 -> 0
            _ -> 1
    , \x -> case x of
            -1 -> -1
            _ -> 1
    , \x -> case x of
            0 -> 0
            2 -> 0
            _ -> 1
    , \x -> case x of
            1 -> 0
            -1 -> 0
            _ -> 1
    , \x -> case x of
            -2 -> 0
            _ -> 1
    , \x -> case x of
            0 -> 2
            _ -> -1
    , \x -> case x of
            0 -> 0
            1 -> 1
            _ -> -1
    , \x -> case x of
            0 -> 1
            1 -> 0
            _ -> -1
    , \x -> case x of
            -1 -> 1
            _ -> -1
    , \x -> case x of
            0 -> 0
            -1 -> 0
            _ -> -1
    , \x -> case x of
            2 -> 0
            _ -> -1
    , \x -> case x of
            0 -> -1
            _ -> 2
    , \x -> case x of
            1 -> 1
            _ -> 2
    , \x -> case x of
            0 -> 0
            1 -> 0
            _ -> 2
    , \x -> case x of
            -1 -> 0
            _ -> 2
    , \x -> case x of
            0 -> 1
            _ -> -2
    , \x -> case x of
            1 -> 0
            _ -> -2
    , \x -> case x of
            0 -> 0
            _ -> 3
    , \_ -> -3
    ]
  , [ \x -> case x of
            0 -> -3
            _ -> 0
    , \x -> case x of
            1 -> 3
            _ -> 0
    , \x -> case x of
            0 -> 1
            1 -> 2
            _ -> 0
    , \x -> case x of
            0 -> -1
            1 -> -1
            _ -> 0
    , \x -> case x of
            0 -> 2
            1 -> 1
            _ -> 0
    , \x -> case x of
            -1 -> -2
            _ -> 0
    , \x -> case x of
            0 -> 1
            -1 -> -1
            _ -> 0
    , \x -> case x of
            0 -> -1
            -1 -> 1
            _ -> 0
    , \x -> case x of
            2 -> 2
            _ -> 0
    , \x -> case x of
            0 -> 1
            2 -> 1
            _ -> 0
    , \x -> case x of
            1 -> 1
            -1 -> 1
            _ -> 0
    , \x -> case x of
            -2 -> -1
            _ -> 0
    , \x -> case x of
            3 -> 1
            _ -> 0
    , \x -> case x of
            0 -> 3
            _ -> 1
    , \x -> case x of
            1 -> -2
            _ -> 1
    , \x -> case x of
            0 -> 0
            1 -> 2
            _ -> 1
    , \x -> case x of
            0 -> 2
            1 -> 0
            _ -> 1
    , \x -> case x of
            -1 -> 2
            _ -> 1
    , \x -> case x of
            0 -> 0
            -1 -> -1
            _ -> 1
    , \x -> case x of
            0 -> -1
            -1 -> 0
            _ -> 1
    , \x -> case x of
            2 -> -1
            _ -> 1
    , \x -> case x of
            0 -> 0
            1 -> 0
            -1 -> 0
            _ -> 1
    , \x -> case x of
            0 -> 0
            -2 -> 0
            _ -> 1
    , \x -> case x of
            1 -> 0
            2 -> 0
            _ -> 1
    , \x -> case x of
            3 -> 0
            _ -> 1
    , \x -> case x of
            0 -> -2
            _ -> -1
    , \x -> case x of
            1 -> 2
            _ -> -1
    , \x -> case x of
            0 -> 1
            1 -> 1
            _ -> -1
    , \x -> case x of
            0 -> 0
            -1 -> 1
            _ -> -1
    , \x -> case x of
            0 -> 1
            -1 -> 0
            _ -> -1
    , \x -> case x of
            2 -> 1
            _ -> -1
    , \x -> case x of
            0 -> 0
            2 -> 0
            _ -> -1
    , \x -> case x of
            1 -> 0
            -1 -> 0
            _ -> -1
    , \x -> case x of
            -2 -> 0
            _ -> -1
    , \x -> case x of
            1 -> -1
            _ -> 2
    , \x -> case x of
            0 -> 0
            1 -> 1
            _ -> 2
    , \x -> case x of
            0 -> 1
            1 -> 0
            _ -> 2
    , \x -> case x of
            -1 -> 1
            _ -> 2
    , \x -> case x of
            0 -> 0
            -1 -> 0
            _ -> 2
    , \x -> case x of
            2 -> 0
            _ -> 2
    , \x -> case x of
            0 -> -1
            _ -> -2
    , \x -> case x of
            1 -> 1
            _ -> -2
    , \x -> case x of
            0 -> 0
            1 -> 0
            _ -> -2
    , \x -> case x of
            -1 -> 0
            _ -> -2
    , \x -> case x of
            0 -> 1
            _ -> 3
    , \x -> case x of
            1 -> 0
            _ -> 3
    , \x -> case x of
            0 -> 0
            _ -> -3
    , \_ -> 4
    ]
  , [ \x -> case x of
            0 -> 4
            _ -> 0
    , \x -> case x of
            1 -> -3
            _ -> 0
    , \x -> case x of
            0 -> 1
            1 -> -2
            _ -> 0
    , \x -> case x of
            0 -> -1
            1 -> 2
            _ -> 0
    , \x -> case x of
            0 -> 2
            1 -> -1
            _ -> 0
    , \x -> case x of
            0 -> -2
            1 -> 1
            _ -> 0
    , \x -> case x of
            -1 -> 3
            _ -> 0
    , \x -> case x of
            0 -> 1
            -1 -> 2
            _ -> 0
    , \x -> case x of
            0 -> -1
            -1 -> -1
            _ -> 0
    , \x -> case x of
            0 -> 2
            -1 -> 1
            _ -> 0
    , \x -> case x of
            2 -> -2
            _ -> 0
    , \x -> case x of
            0 -> 1
            2 -> -1
            _ -> 0
    , \x -> case x of
            0 -> -1
            2 -> 1
            _ -> 0
    , \x -> case x of
            1 -> 1
            -1 -> -1
            _ -> 0
    , \x -> case x of
            1 -> -1
            -1 -> 1
            _ -> 0
    , \x -> case x of
            -2 -> 2
            _ -> 0
    , \x -> case x of
            0 -> 1
            -2 -> 1
            _ -> 0
    , \x -> case x of
            1 -> 1
            2 -> 1
            _ -> 0
    , \x -> case x of
            3 -> -1
            _ -> 0
    , \x -> case x of
            -3 -> 1
            _ -> 0
    , \x -> case x of
            0 -> -3
            _ -> 1
    , \x -> case x of
            1 -> 3
            _ -> 1
    , \x -> case x of
            0 -> 0
            1 -> -2
            _ -> 1
    , \x -> case x of
            0 -> -1
            1 -> -1
            _ -> 1
    , \x -> case x of
            0 -> -2
            1 -> 0
            _ -> 1
    , \x -> case x of
            -1 -> -2
            _ -> 1
    , \x -> case x of
            0 -> 0
            -1 -> 2
            _ -> 1
    , \x -> case x of
            0 -> 2
            -1 -> 0
            _ -> 1
    , \x -> case x of
            2 -> 2
            _ -> 1
    , \x -> case x of
            0 -> 0
            2 -> -1
            _ -> 1
    , \x -> case x of
            0 -> -1
            2 -> 0
            _ -> 1
    , \x -> case x of
            1 -> 0
            -1 -> -1
            _ -> 1
    , \x -> case x of
            1 -> -1
            -1 -> 0
            _ -> 1
    , \x -> case x of
            -2 -> -1
            _ -> 1
    , \x -> case x of
            0 -> 0
            1 -> 0
            2 -> 0
            _ -> 1
    , \x -> case x of
            0 -> 0
            3 -> 0
            _ -> 1
    , \x -> case x of
            1 -> 0
            -2 -> 0
            _ -> 1
    , \x -> case x of
            -1 -> 0
            2 -> 0
            _ -> 1
    , \x -> case x of
            -3 -> 0
            _ -> 1
    , \x -> case x of
            0 -> 3
            _ -> -1
    , \x -> case x of
            1 -> -2
            _ -> -1
    , \x -> case x of
            0 -> 0
            1 -> 2
            _ -> -1
    , \x -> case x of
            0 -> 2
            1 -> 0
            _ -> -1
    , \x -> case x of
            -1 -> 2
            _ -> -1
    , \x -> case x of
            0 -> 1
            -1 -> 1
            _ -> -1
    , \x -> case x of
            0 -> 0
            2 -> 1
            _ -> -1
    , \x -> case x of
            0 -> 1
            2 -> 0
            _ -> -1
    , \x -> case x of
            1 -> 0
            -1 -> 1
            _ -> -1
    , \x -> case x of
            1 -> 1
            -1 -> 0
            _ -> -1
    , \x -> case x of
            -2 -> 1
            _ -> -1
    , \x -> case x of
            0 -> 0
            1 -> 0
            -1 -> 0
            _ -> -1
    , \x -> case x of
            0 -> 0
            -2 -> 0
            _ -> -1
    , \x -> case x of
            1 -> 0
            2 -> 0
            _ -> -1
    , \x -> case x of
            3 -> 0
            _ -> -1
    , \x -> case x of
            0 -> -2
            _ -> 2
    , \x -> case x of
            0 -> 0
            1 -> -1
            _ -> 2
    , \x -> case x of
            0 -> 1
            1 -> 1
            _ -> 2
    , \x -> case x of
            0 -> -1
            1 -> 0
            _ -> 2
    , \x -> case x of
            -1 -> -1
            _ -> 2
    , \x -> case x of
            0 -> 0
            -1 -> 1
            _ -> 2
    , \x -> case x of
            0 -> 1
            -1 -> 0
            _ -> 2
    , \x -> case x of
            2 -> 1
            _ -> 2
    , \x -> case x of
            0 -> 0
            2 -> 0
            _ -> 2
    , \x -> case x of
            1 -> 0
            -1 -> 0
            _ -> 2
    , \x -> case x of
            -2 -> 0
            _ -> 2
    , \x -> case x of
            0 -> 2
            _ -> -2
    , \x -> case x of
            1 -> -1
            _ -> -2
    , \x -> case x of
            0 -> 0
            1 -> 1
            _ -> -2
    , \x -> case x of
            0 -> 1
            1 -> 0
            _ -> -2
    , \x -> case x of
            -1 -> 1
            _ -> -2
    , \x -> case x of
            0 -> 0
            -1 -> 0
            _ -> -2
    , \x -> case x of
            2 -> 0
            _ -> -2
    , \x -> case x of
            0 -> -1
            _ -> 3
    , \x -> case x of
            1 -> 1
            _ -> 3
    , \x -> case x of
            0 -> 0
            1 -> 0
            _ -> 3
    , \x -> case x of
            -1 -> 0
            _ -> 3
    , \x -> case x of
            0 -> 1
            _ -> -3
    , \x -> case x of
            1 -> 0
            _ -> -3
    , \x -> case x of
            0 -> 0
            _ -> 4
    , \_ -> -4
    ]
  , ...
  ]