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 MainClass
{
    public static void Main(string[] args)
    {
        var x = int.Parse(Console.ReadLine());

        var d = new bool[100005];

        for (int i = 2; i < d.Length; i++)
        {
            for (int j = 2; i * j < d.Length; j++)
            {
                d[i * j] = true;
            }
        }

        for (int i = x; i < d.Length; i++)
        {
            if (!d[i])
            {
                Console.WriteLine(i);
                return;
            }
        }
    }
}