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# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;

namespace atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var ps = new List<int>();
            for (var i = 2;; i += 2)
            {
                var isPrime = true;
                var sqrtI = Math.Sqrt(i);
                foreach (var p in ps)
                {
                    if (i % p == 0)
                    {
                        isPrime = false;
                        break;
                    }
                    else if (p > sqrtI)
                    {
                        break;
                    }
                }
                if (isPrime)
                {
                    if (i >= n)
                    {

                        Console.WriteLine(i);
                        return;
                    }
                    else
                        ps.Add(i);
                }
            }
        }
    }
}