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

#include <iostream>
#include <cmath>
using namespace std;

bool primeCheck(int n, int k) {
  if (k == 1) return true;
  return (n % k != 0) && primeCheck(n, k - 1);
}

int leastPrime(int n) {
  return primeCheck(n, sqrt(n))? n: leastPrime(n + 1);
}

int main() {
  int n; cin >> n;
  cout << leastPrime(n);
  return 0;
}