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;

int main() {
  int x;
  cin>>x;
  
  vector<bool> p(x+1001,true);
  p[0] = p[1] = false;
  
  for(int i=3; i<x+1001; i+=2) {
    if(p[i]) {
      for(int j=i*i; j<x+1001; j+=i)
        p[i] = false;
    }
  }
  
  for(int i=x; i<x+1001; i++) {
    if(i%2 && p[i]) {
      cout<<i<<endl;
      break;
    }
  }
  
  return 0;
}