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)

primes :: [Int]
primes = 2 : f [3] [3,5..]
  where
    f [] _ = []
    f (x:xs) ys =
        let (ps, qs) = span (< x^2) ys
         in ps ++ f (xs ++ ps) [z | z <- qs, z `rem` x /= 0]

main :: IO ()
main = do
    x <- readLn :: IO Int
    print . head . dropWhile (x>) $ primes