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;
class Program
{
	static void Main(string[] args)
	{
		int input = int.Parse(Console.ReadLine());
		for(int i=input;true;i++){
			if(IsPrime(i)){
				Console.WriteLine(i);
				break;
			}
		}
	}
	public static bool IsPrime(int num)
	{
	    if (num < 2) return false;
	    else if (num == 2) return true;
	    else if (num % 2 == 0) return false; // 偶数はあらかじめ除く
	
	    double sqrtNum = Math.Sqrt(num);
	    for (int i = 3; i <= sqrtNum; i += 2)
	    {
	        if (num % i == 0)
	        {
	            // 素数ではない
	            return false;
	        }
	    }
	
	    // 素数である
	    return true;
	}
}