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.Linq;
using System.Collections.Generic;

using E = System.Linq.Enumerable;

public class Program
{
    public static void Main()
    {
        var xx = int.Parse(Console.ReadLine());

        var xs = new int[xx];
        xs[0] = 2;
        for (int i = 1; i < xs.Length; ++i)
        {
            xs[i] = (i + 1) * 2 + 1;
        }
        int r = 0;
        int last = xs.Length;
        while (xs[0] < xx)
        {
            for (int i = 1; i < last; ++i)
            {
                var s = xs[i];
                if (s % xs[0] != 0)
                {
                    xs[r++] = s;
                }
            }
            last = r;
            r = 1;
            xs[0] = xs[1];
        }

        Console.WriteLine(xs[0]);
    }
}