map length (tiers :: [[ Nat->Nat ]])  =  [2,3,8,20,61,204,...]

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

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

ratioRepetitions (list :: [ Nat->Nat ])  =  85 % 149

tiers :: [Nat->Nat]  =
  [ [ \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    ]
  , [ \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 1
              3 -> 1
              4 -> 1
              5 -> 1
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 1
              3 -> 1
              4 -> 1
              5 -> 1
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    ]
  , [ \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 1
              3 -> 1
              4 -> 1
              5 -> 1
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 2
              1 -> 2
              2 -> 2
              3 -> 2
              4 -> 2
              5 -> 2
              6 -> 2
              7 -> 2
              ...
    , \x -> case x of
              0 -> 2
              1 -> 2
              2 -> 2
              3 -> 2
              4 -> 2
              5 -> 2
              6 -> 2
              7 -> 2
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    ]
  , [ \x -> case x of
              0 -> 2
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 1
              4 -> 1
              5 -> 1
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 2
              2 -> 2
              3 -> 2
              4 -> 2
              5 -> 2
              6 -> 2
              7 -> 2
              ...
    , \x -> case x of
              0 -> 3
              1 -> 3
              2 -> 3
              3 -> 3
              4 -> 3
              5 -> 3
              6 -> 3
              7 -> 3
              ...
    , \x -> case x of
              0 -> 3
              1 -> 3
              2 -> 3
              3 -> 3
              4 -> 3
              5 -> 3
              6 -> 3
              7 -> 3
              ...
    , \x -> case x of
              0 -> 0
              1 -> 2
              2 -> 0
              3 -> 2
              4 -> 0
              5 -> 2
              6 -> 0
              7 -> 2
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 1
              3 -> 1
              4 -> 1
              5 -> 1
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 2
              1 -> 0
              2 -> 2
              3 -> 0
              4 -> 2
              5 -> 0
              6 -> 2
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    ]
  , [ \x -> case x of
              0 -> 3
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 2
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 2
              1 -> 1
              2 -> 1
              3 -> 1
              4 -> 1
              5 -> 1
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
              3 -> 1
              4 -> 1
              5 -> 1
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 1
              5 -> 1
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 1
              1 -> 2
              2 -> 2
              3 -> 2
              4 -> 2
              5 -> 2
              6 -> 2
              7 -> 2
              ...
    , \x -> case x of
              0 -> 2
              1 -> 0
              2 -> 2
              3 -> 2
              4 -> 2
              5 -> 2
              6 -> 2
              7 -> 2
              ...
    , \x -> case x of
              0 -> 0
              1 -> 3
              2 -> 3
              3 -> 3
              4 -> 3
              5 -> 3
              6 -> 3
              7 -> 3
              ...
    , \x -> case x of
              0 -> 4
              1 -> 4
              2 -> 4
              3 -> 4
              4 -> 4
              5 -> 4
              6 -> 4
              7 -> 4
              ...
    , \x -> case x of
              0 -> 4
              1 -> 4
              2 -> 4
              3 -> 4
              4 -> 4
              5 -> 4
              6 -> 4
              7 -> 4
              ...
    , \x -> case x of
              0 -> 0
              1 -> 3
              2 -> 0
              3 -> 3
              4 -> 0
              5 -> 3
              6 -> 0
              7 -> 3
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 2
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 2
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 2
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 2
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 2
              2 -> 1
              3 -> 2
              4 -> 1
              5 -> 2
              6 -> 1
              7 -> 2
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 1
              4 -> 1
              5 -> 0
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 1
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 2
              2 -> 0
              3 -> 2
              4 -> 0
              5 -> 2
              6 -> 0
              7 -> 2
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 2
              1 -> 1
              2 -> 2
              3 -> 1
              4 -> 2
              5 -> 1
              6 -> 2
              7 -> 1
              ...
    , \x -> case x of
              0 -> 2
              1 -> 0
              2 -> 2
              3 -> 0
              4 -> 2
              5 -> 0
              6 -> 2
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 1
              3 -> 1
              4 -> 0
              5 -> 1
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 1
              5 -> 1
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 3
              1 -> 0
              2 -> 3
              3 -> 0
              4 -> 3
              5 -> 0
              6 -> 3
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 2
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 2
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 2
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 2
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    ]
  , [ \x -> case x of
              0 -> 4
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 3
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 2
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 3
              1 -> 1
              2 -> 1
              3 -> 1
              4 -> 1
              5 -> 1
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 1
              1 -> 2
              2 -> 1
              3 -> 1
              4 -> 1
              5 -> 1
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 1
              5 -> 1
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 1
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 2
              1 -> 1
              2 -> 2
              3 -> 2
              4 -> 2
              5 -> 2
              6 -> 2
              7 -> 2
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 2
              3 -> 2
              4 -> 2
              5 -> 2
              6 -> 2
              7 -> 2
              ...
    , \x -> case x of
              0 -> 2
              1 -> 2
              2 -> 0
              3 -> 2
              4 -> 2
              5 -> 2
              6 -> 2
              7 -> 2
              ...
    , \x -> case x of
              0 -> 1
              1 -> 3
              2 -> 3
              3 -> 3
              4 -> 3
              5 -> 3
              6 -> 3
              7 -> 3
              ...
    , \x -> case x of
              0 -> 3
              1 -> 0
              2 -> 3
              3 -> 3
              4 -> 3
              5 -> 3
              6 -> 3
              7 -> 3
              ...
    , \x -> case x of
              0 -> 0
              1 -> 4
              2 -> 4
              3 -> 4
              4 -> 4
              5 -> 4
              6 -> 4
              7 -> 4
              ...
    , \x -> case x of
              0 -> 5
              1 -> 5
              2 -> 5
              3 -> 5
              4 -> 5
              5 -> 5
              6 -> 5
              7 -> 5
              ...
    , \x -> case x of
              0 -> 5
              1 -> 5
              2 -> 5
              3 -> 5
              4 -> 5
              5 -> 5
              6 -> 5
              7 -> 5
              ...
    , \x -> case x of
              0 -> 0
              1 -> 4
              2 -> 0
              3 -> 4
              4 -> 0
              5 -> 4
              6 -> 0
              7 -> 4
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 3
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 3
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 2
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 2
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 2
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 2
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 2
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 2
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 2
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 2
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 2
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 2
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 3
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 3
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 2
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 2
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 3
              2 -> 1
              3 -> 3
              4 -> 1
              5 -> 3
              6 -> 1
              7 -> 3
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 2
              4 -> 1
              5 -> 0
              6 -> 1
              7 -> 2
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 1
              4 -> 1
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 1
              3 -> 1
              4 -> 1
              5 -> 1
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 1
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 1
              4 -> 1
              5 -> 0
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 2
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 2
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 1
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 3
              2 -> 0
              3 -> 3
              4 -> 0
              5 -> 3
              6 -> 0
              7 -> 3
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 2
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 2
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 2
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 2
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 2
              1 -> 2
              2 -> 2
              3 -> 2
              4 -> 2
              5 -> 2
              6 -> 2
              7 -> 2
              ...
    , \x -> case x of
              0 -> 2
              1 -> 0
              2 -> 2
              3 -> 1
              4 -> 2
              5 -> 0
              6 -> 2
              7 -> 1
              ...
    , \x -> case x of
              0 -> 2
              1 -> 0
              2 -> 2
              3 -> 0
              4 -> 2
              5 -> 0
              6 -> 2
              7 -> 0
              ...
    , \x -> case x of
              0 -> 2
              1 -> 1
              2 -> 2
              3 -> 0
              4 -> 2
              5 -> 1
              6 -> 2
              7 -> 0
              ...
    , \x -> case x of
              0 -> 2
              1 -> 0
              2 -> 2
              3 -> 0
              4 -> 2
              5 -> 0
              6 -> 2
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 2
              2 -> 1
              3 -> 2
              4 -> 0
              5 -> 2
              6 -> 1
              7 -> 2
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
              3 -> 1
              4 -> 0
              5 -> 0
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 1
              3 -> 0
              4 -> 0
              5 -> 1
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 2
              2 -> 0
              3 -> 2
              4 -> 0
              5 -> 2
              6 -> 0
              7 -> 2
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 2
              2 -> 0
              3 -> 2
              4 -> 1
              5 -> 2
              6 -> 0
              7 -> 2
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 0
              3 -> 1
              4 -> 1
              5 -> 0
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 0
              3 -> 0
              4 -> 1
              5 -> 1
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 2
              2 -> 0
              3 -> 2
              4 -> 0
              5 -> 2
              6 -> 0
              7 -> 2
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 3
              1 -> 1
              2 -> 3
              3 -> 1
              4 -> 3
              5 -> 1
              6 -> 3
              7 -> 1
              ...
    , \x -> case x of
              0 -> 3
              1 -> 0
              2 -> 3
              3 -> 0
              4 -> 3
              5 -> 0
              6 -> 3
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 2
              3 -> 1
              4 -> 0
              5 -> 1
              6 -> 2
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 2
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 2
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 1
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 1
              3 -> 1
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 1
              3 -> 1
              4 -> 1
              5 -> 1
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 1
              5 -> 1
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 1
              3 -> 1
              4 -> 0
              5 -> 1
              6 -> 1
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 2
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 2
              5 -> 1
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 2
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 2
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 1
              5 -> 1
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 1
              2 -> 0
              3 -> 1
              4 -> 0
              5 -> 1
              6 -> 0
              7 -> 1
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 4
              1 -> 0
              2 -> 4
              3 -> 0
              4 -> 4
              5 -> 0
              6 -> 4
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 3
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 3
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 2
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 2
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 2
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 2
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 2
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 2
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 2
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 2
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 2
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 2
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 1
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 1
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 3
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 3
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 2
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 1
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 2
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 1
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    , \x -> case x of
              0 -> 0
              1 -> 0
              2 -> 0
              3 -> 0
              4 -> 0
              5 -> 0
              6 -> 0
              7 -> 0
              ...
    ]
  , ...
  ]