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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
using graph = vector<vector<ll>>;
int prime(int x) {
	int a = x - 1;
	while (a >= pow(x, 0.5)) {
		if (x % a == 0) {
			return 1;
			break;
		}
		a--;
	}
	return 0;
}

int main() {
	ll x;
	cin >> x;
	while (prime(x) == 1) {
		x++;
	}
	cout << x << endl;
	return 0;
}