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;

#define rep(i,n) for(long long i=0; i<(long long)(n);i++)
#define rep2(i,s,n) for(long long i=(s); i<(long long)(n);i++)

#define mod 1e9+7;
#define inf 1e18+7;

typedef long long ll;

int main() {
    int x;
    cin>>x;

    if(x<=3){
        cout<<x<<endl;
        return 0;
    }

    if(x%2==0){
        x++;
    }

    for(int i=x;i<=100003;i+=2){
        bool jdg=true;
        for(int j=3;j<=sqrt(i);j+=2){
            if(i%j==0){
                jdg=false;
                break;
            }
        }
        if(jdg){
            cout<<i<<endl;
            return 0;
        }
    }
}