map length (tiers :: [[ (Nat,Nat)->Nat ]])  =  [2,4,14,53,...]

length (list :: [ (Nat,Nat)->Nat ])  =  Infinity

allUnique (list :: [ (Nat,Nat)->Nat ])  =  False

ratioRepetitions (list :: [ (Nat,Nat)->Nat ])  =  41 % 73

tiers :: [(Nat,Nat)->Nat]  =
  [ [ \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    ]
  , [ \x -> case x of
              (0,0) -> 1
              (0,1) -> 1
              (1,0) -> 1
              (0,2) -> 1
              (1,1) -> 1
              (2,0) -> 1
              (0,3) -> 1
              (1,2) -> 1
              ...
    , \x -> case x of
              (0,0) -> 1
              (0,1) -> 1
              (1,0) -> 1
              (0,2) -> 1
              (1,1) -> 1
              (2,0) -> 1
              (0,3) -> 1
              (1,2) -> 1
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    ]
  , [ \x -> case x of
              (0,0) -> 1
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 1
              (1,0) -> 1
              (0,2) -> 1
              (1,1) -> 1
              (2,0) -> 1
              (0,3) -> 1
              (1,2) -> 1
              ...
    , \x -> case x of
              (0,0) -> 2
              (0,1) -> 2
              (1,0) -> 2
              (0,2) -> 2
              (1,1) -> 2
              (2,0) -> 2
              (0,3) -> 2
              (1,2) -> 2
              ...
    , \x -> case x of
              (0,0) -> 2
              (0,1) -> 2
              (1,0) -> 2
              (0,2) -> 2
              (1,1) -> 2
              (2,0) -> 2
              (0,3) -> 2
              (1,2) -> 2
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 1
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 1
              (2,0) -> 0
              (0,3) -> 1
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 1
              (0,1) -> 0
              (1,0) -> 1
              (0,2) -> 1
              (1,1) -> 0
              (2,0) -> 1
              (0,3) -> 0
              (1,2) -> 1
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 1
              (0,2) -> 0
              (1,1) -> 1
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 1
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 1
              (0,1) -> 1
              (1,0) -> 0
              (0,2) -> 1
              (1,1) -> 0
              (2,0) -> 1
              (0,3) -> 1
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    ]
  , [ \x -> case x of
              (0,0) -> 2
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 1
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 1
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 1
              (0,1) -> 0
              (1,0) -> 1
              (0,2) -> 1
              (1,1) -> 1
              (2,0) -> 1
              (0,3) -> 1
              (1,2) -> 1
              ...
    , \x -> case x of
              (0,0) -> 1
              (0,1) -> 1
              (1,0) -> 0
              (0,2) -> 1
              (1,1) -> 1
              (2,0) -> 1
              (0,3) -> 1
              (1,2) -> 1
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 2
              (1,0) -> 2
              (0,2) -> 2
              (1,1) -> 2
              (2,0) -> 2
              (0,3) -> 2
              (1,2) -> 2
              ...
    , \x -> case x of
              (0,0) -> 3
              (0,1) -> 3
              (1,0) -> 3
              (0,2) -> 3
              (1,1) -> 3
              (2,0) -> 3
              (0,3) -> 3
              (1,2) -> 3
              ...
    , \x -> case x of
              (0,0) -> 3
              (0,1) -> 3
              (1,0) -> 3
              (0,2) -> 3
              (1,1) -> 3
              (2,0) -> 3
              (0,3) -> 3
              (1,2) -> 3
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 2
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 2
              (2,0) -> 0
              (0,3) -> 2
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 1
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 1
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 1
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 1
              (0,1) -> 1
              (1,0) -> 1
              (0,2) -> 1
              (1,1) -> 1
              (2,0) -> 1
              (0,3) -> 1
              (1,2) -> 1
              ...
    , \x -> case x of
              (0,0) -> 1
              (0,1) -> 0
              (1,0) -> 1
              (0,2) -> 1
              (1,1) -> 0
              (2,0) -> 1
              (0,3) -> 0
              (1,2) -> 1
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 1
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 1
              (2,0) -> 0
              (0,3) -> 1
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 2
              (0,1) -> 0
              (1,0) -> 2
              (0,2) -> 2
              (1,1) -> 0
              (2,0) -> 2
              (0,3) -> 0
              (1,2) -> 2
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 1
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 1
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 1
              (0,1) -> 0
              (1,0) -> 1
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 1
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 2
              (0,2) -> 0
              (1,1) -> 2
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 2
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 1
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 1
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 1
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 1
              (0,2) -> 0
              (1,1) -> 1
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 1
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 1
              (0,1) -> 1
              (1,0) -> 1
              (0,2) -> 1
              (1,1) -> 1
              (2,0) -> 1
              (0,3) -> 1
              (1,2) -> 1
              ...
    , \x -> case x of
              (0,0) -> 1
              (0,1) -> 1
              (1,0) -> 0
              (0,2) -> 1
              (1,1) -> 0
              (2,0) -> 1
              (0,3) -> 1
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 1
              (0,1) -> 1
              (1,0) -> 0
              (0,2) -> 1
              (1,1) -> 0
              (2,0) -> 1
              (0,3) -> 1
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 1
              (0,2) -> 0
              (1,1) -> 1
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 1
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 1
              (0,2) -> 0
              (1,1) -> 1
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 1
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 2
              (0,1) -> 2
              (1,0) -> 0
              (0,2) -> 2
              (1,1) -> 0
              (2,0) -> 2
              (0,3) -> 2
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 1
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 1
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 1
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 1
              (1,1) -> 0
              (2,0) -> 1
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 1
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 1
              (0,1) -> 1
              (1,0) -> 0
              (0,2) -> 1
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 1
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    , \x -> case x of
              (0,0) -> 0
              (0,1) -> 0
              (1,0) -> 0
              (0,2) -> 0
              (1,1) -> 0
              (2,0) -> 0
              (0,3) -> 0
              (1,2) -> 0
              ...
    ]
  , ...
  ]