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: Wrong Answer)

import           Control.Monad
import qualified Data.ByteString.Char8 as BS
import           Data.List
import           Data.Maybe
import           Debug.Trace

readInt = fst . fromJust . BS.readInt
getInt = readInt <$> BS.getLine

isPrime x | x < 2 = False
          | otherwise = let sx = ceiling $ sqrt $ fromIntegral x
                        in and [x `mod` i /= 0 | i <- [2..sx]]

solve n | isPrime n = n
        | otherwise = solve (n+1)

main = do
  x <- getInt
  let ans = solve x
  print ans