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)

module Main where
import           Control.Applicative

main :: IO ()
main = do
    input <- read <$> getLine
    putStrLn . show $ nextPrime input


isPrime :: Int -> Bool
isPrime x | x < 2     = False
          | otherwise = prime (2 : [3, 4 .. (x - 1)])
  where
    prime :: [Int] -> Bool
    prime [] = True
    prime (t : next) | t == 2 = True
                     | x `mod` t == 0 = False
                     | otherwise      = prime next

nextPrime :: Int -> Int
nextPrime n = if isPrime n then n else nextPrime (n + 1)