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 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(int)(n);i++)
using namespace std;

using ll = long long;

const int INF = 1001001001;
const ll INF_LL = 1001001001001001001LL;

int main(void){
  int x; cin >> x;
  int M = 1000000;

  for(int i = x;i<M;++i){
    bool prime = true;
    for(int j = 2;j<i;++j){
      if(i%j==0){
	prime = false;
	break;
      }
    }
    if(prime){
      cout << i << endl;
      return 0;
    }
  }
  
  return 0;
}