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)

import Control.Applicative
import Control.Monad
import Control.Monad.ST
import Data.Vector.Unboxed.Mutable (STVector)
import qualified Data.Vector.Unboxed.Mutable as VM

main :: IO ()
main = solve <$> readLn >>= print

solve :: Int -> Int
solve n = runST $ do
  sv <- sieve 100003
  loop sv n
  where
    loop sv i = do
      b <- VM.read sv i
      if b then return i
        else loop sv (i + 1)

sieve :: Int -> ST s (STVector s Bool)
sieve n = do
  sv <- VM.replicate (n + 1) True
  VM.write sv 0 False
  VM.write sv 1 False
  forM_ ixs $ \i -> do
    b <- VM.read sv i
    when b $ forM_ [i * i, i * i + i .. n] $ \j -> VM.write sv j False
  return sv
  where
    ixs = takeWhile ((<= n) . (^2)) [2..]