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;
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
typedef long long int ll;
typedef pair<int, int> P;

const int MAX = 123456;
vector<bool> pn(MAX, true);

void init(){
  pn[0] = pn[1] = false;
  for(int i = 4; i < MAX; i += 2){
    pn[i] = false;
  }
  for(int i = 3; i <= sqrt(MAX); i += 2){
    for(int j = i * 2; j < MAX; j += i){
      pn[j] = false;
    }
  }
}

int x;

int main(){
  init();
  cin >> x;
  while(true){
    x++;
    if(pn[x]){
      cout << x << endl;
      break;
    }
  }
  return 0;
}