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<(n);i++)
#define REP(i,n) for(int i=1;i<=(n);i++)
typedef long long ll;
typedef pair<int,int> pii;

const int max_n = 100005;
int a[max_n];

int main(){
    int n;
    cin >> n;
    for(int i=2;i<n+1;i++){
        if(a[i]==0){
            int tmp = max_n/i;
            for(int j=1; j<=tmp ;j++){
                a[j*i] = 1;
            }
        }
    }
    for(int i=n;i<max_n;i++){
        if(a[i]==0) {
            cout << i <<endl;
            return 0;    
        }
    }
    return 0;
}