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

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

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

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

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