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 <string>
#include <vector>
#include <algorithm>
#include <cmath>
using namespace std;

bool is_prime(int n) {
    bool isPrime = true;
    for (int i = 2; i < sqrt(n); ++i) {
        if (n % i == 0) {
            isPrime = false;
        }
    }

    return isPrime;
}

int next_prime(int n) {
    int p = n;
    while (! is_prime(p)) {
        ++p;
    }

    return p;
}

int main () {
    int n;
    cin >> n;

    cout << next_prime(n) << endl;
    
    return 0;
}