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 <bits/stdc++.h>
using namespace std;


int main() {
  int n;
  int a;

  cin >> n;
  
  a = n;
  while (n > 2) {
    if (a % 2 == 0) {
      a++;
      continue;
    }
    int n1 = sqrt(a);
    int flag = 0;
    for (int i = 3; i <= n1; i += 2) {
      if (a % i == 0) {
        flag = 1;
        break;
      }
    }
    if (flag == 0) {
      break;
    }
    a++;
  }
  cout << a << endl;
}