map length (tiers :: [[ [Int]->[Int] ]])  =  [1,1,4,10,29,75,...]

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

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

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

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