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: Runtime Error)

#include<bits/stdc++.h>
#define ll long long
#define pii pair<int,int>
#define pb push_back
#define f first
#define s second
#define MOD 1000000007
 
using namespace std;

bool prime[200001];

void solve(){
	ll x; cin>>x;
	
	for(int i=2; i<200001; i++){
		if(!prime[i]){
			for(int j=i; i*j<=200000; j++){
				prime[j*i] = 1;
			}
		}
	}
	for(int i=2; i<=200000; i++){
		if(prime[i] == 0 && i>=x){
			cout<<i; break;
		}
	}


}


int main()
{ 
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	//cout<<fixed<<setprecision(12);
	
	int t =1; 
	//cin>>t;

	for(int i=1; i<=t; i++){
		solve();
		cout<<"\n";
	}
	return 0;

}