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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
using vi = vector<int>;
using vii = vector<vi>;
using in6 = int64_t;
using ind = double;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)

vi prime(int x) {
  vi data;
  data.push_back(2);
  data.push_back(3);
  int a = 5;
  while(data.size() <= x) {
    bool check = true;
    for(int i = 2; i * i < a; i++) {
      if(a % i == 0) {
        check = false;
        break;
      }
    }
    if(check) data.push_back(a);
    a++;
  }
  return data;
}

int main() {
  int n;
  vi data = prime(n);
  int ans = 0;
  int i = 0;
  while (ans == 0) {
    if(data[i] <= n && data[i + 1] > n) ans = data[i + 1];
    else i++;
  }
  cout << ans << endl;
}