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 OCaml (4.02.3) (judge verdict: Accepted)

let rec fix f x = f (fix f) x
let isprime x =
  fix (fun f d -> if d * d > x then true else x mod d <> 0 && f (d+1)) 2

let () =
  Scanf.scanf "%d" @@ fun x ->
  fix (fun f v -> if isprime v then v else f (v+1)) x
  |> Printf.printf "%d\n"