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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace C
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var x = int.Parse(Console.ReadLine());

            while (true)
            {
                if (IsPrime(x))
                {
                    Console.WriteLine(x);
                    break;
                }
                x++;
            }
        }

        static bool IsPrime(int x)
        {
            if (x < 2) return false;
            if (x == 2) return true;
            if (x % 2 == 0) return false;
            var sqrt = Math.Sqrt(x);
            for (var i = 3; i < sqrt; i++) if (x % i == 0) return false;
            return true;
        }
    }
}