data E = Sevens Int | E :+: E | E :-: E | E :*: E | E :/: E | Neg E
 
eval :: E -> Double
eval (Sevens k) = (iterate (\x -> 14*x + 7) 0) !! k
eval (a :+: b)  = (eval a) + (eval b)
eval (a :-: b)  = (eval a) - (eval b)
eval (a :*: b)  = (eval a) * (eval b)
eval (a :/: b)  = (eval a) / (eval b)
eval (Neg a)    = -(eval a)
 
showE :: Int -> E -> String
showE pe = s pe
  where s pe (Sevens k) = take k (repeat '7')
        s pe (a:+:b) = helper pe 1 a b "+"
        s pe (a:-:b) = helper pe 2 a b "-"
        s pe (a:*:b) = helper pe 3 a b "*"
        s pe (a:/:b) = helper pe 4 a b "/"
        s pe (Neg a) = "-" ++ (s 2 a)
        helper pe p a b op
          | p > pe    = (s p a) ++ op ++ (s p b)
          | otherwise = "(" ++ (s p a) ++ op ++ (s p b) ++ ")"
 
instance Show E where
  show = showE 0
 
anyE :: Int -> [E]
anyE n = let xs = f n in xs ++ map Neg xs
  where f n = (Sevens n) : do
                k  <- [1..n-1]
                a  <- f k
                b  <- f (n-k)
                op <- if k <= n-k then [ (:+:), (:-:), (:*:), (:/:) ]
                                  else [ (:-:), (:/:) ]
                return (op a b)
 
main = mapM_ print (filter check (anyE 5))
  where check e = (abs ((eval e) - 14*14)) < 1e-7
 

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