-- | Generates the sequence of prime numbers. -- Based on . primes :: Integral a => [a] primes = map fromIntegral primes' where primes' = [2, 3, 5] ++ sieve2 5 7 (drop 2 primes') sieve2 m s (p : ps) = [n | n <- ns, gcd m n == 1] ++ sieve2 (m * p) (p * p) ps where ns = [x + y | x <- [s, s + 6 .. p * p - 2], y <- [0, 4]] -- | Factorizes the given integer using 'primes'. -- Based on . factorize :: Integral a => a -> [a] factorize 1 = [] factorize n = factorize' n primes where factorize' n ps@(p : pr) | p * p > n = [n] | m == 0 = p : factorize' d ps | otherwise = factorize' n pr where (d, m) = divMod n p getMinimum :: Integral a => a -> a getMinimum n | h > 2 = h | elem 3 fs = 3 | notElem 2 fr = head fr | otherwise = 4 where fs@(h : fr) = factorize n main :: IO () main = print . getMinimum =<< readLn