Problem:
Score: 300 points

Problem Statement

Find the minimum prime number greater than or equal to X.

Notes

A prime number is an integer greater than 1 that cannot be evenly divided by any positive integer except 1 and itself.

For example, 2, 3, and 5 are prime numbers, while 4 and 6 are not.

Constraints

2 \le X \le 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X

Output

Print the minimum prime number greater than or equal to X.

Sample Input 1

20

Sample Output 1

23

The minimum prime number greater than or equal to 20 is 23.

Sample Input 2

2

Sample Output 2

2

X itself can be a prime number.

Sample Input 3

99992

Sample Output 3

100003

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

-- [Char]あるいは String を Int にする
toInt :: (String -> Int)
toInt x = read x ::Int

--入力を受け取り、[Int]にする
getInts = do
  x <- getLine
  let y = (map $ toInt) $ words x -- 半角スペースで分割してInt にする
  return y

-- C
divisor :: Int -> [Int]
divisor n = [m | m <- [1..half], n `mod` m == 0]
            where
                half = n `div` 2

prime :: Int -> Bool
prime n = length (divisor n) == 1 

main = do
    x <- readLn :: IO Int
    putStrLn $ show (head $ filter prime [x..])