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)

module Main where

import Data.List
import Control.Monad
import Debug.Trace
import qualified Data.ByteString.Char8 as BC
import Data.Maybe (fromJust)


readTuple2 :: IO (Int, Int)
readTuple2 = do
    [a, b] <- map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine
    return (a, b)

readTuple3 :: IO (Int, Int, Int)
readTuple3 = do
    [a, b, c] <- map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine
    return (a, b, c)

readInt :: IO Int
readInt = fst . fromJust . BC.readInt <$> BC.getLine

readInts :: IO [Int]
readInts = map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine

split :: (a -> Bool) -> [a] -> [[a]]
split f [] = []
split f as = let
    (fo, la) = span f as
    las = case la of
        [] -> []
        xs -> split f $ tail xs
    in
        case fo of
            [] -> las
            xs -> xs : las

isPrime :: Int -> Bool
isPrime 1 = False
isPrime 2 = True
isPrime n
    | even n = False
    | otherwise = all ((/= 0) . (n `mod`)) [2..(ceiling $ sqrt $ fromIntegral n)]

solve :: Int -> Int
solve n = head $ filter isPrime [n..]

main = do
    num <- readInt
    print $ solve num