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"
#define rep(i,n) for(int i=0;i<n;i++)
using namespace std;

typedef long long ll;

const ll MOD = 1e9 + 7;

int main() {
    int X, MAXP = 100004;
    cin >> X;
    vector<bool> p(MAXP, true); 
    for (int i = 2; i * i <= MAXP; i++) {
        if (p[i]) {
            for (int j = i * 2; j <= MAXP; j += i) {
                p[j] = false;
            }
        }
    }
    for (int i = X; i <= MAXP; i++) {
        if (p[i]) {
            cout << i << endl;
            break;
        }
    }
}