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: Runtime Error)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
const ll mod = 1e9 + 7;
bool prime[(int)1e6 + 7];
vector<int> primes;

int main() {
	int x;
	cin >> x;
	for (int i = 2; i <= 1e5 + 7; i++) {
		if (prime[i])
			continue;

		primes.push_back(i);
		if (i > x) {
			break;
		}
		for (ll j = i * i; j <= 1e5 + 7; j += i) {
			prime[j] = 1;
		}
	}

	cout << primes.back();

}