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;

const int MAX = 1000000;
bool A[MAX];

int main() {
    int x;
    cin >> x;
    for (int i = 0; i < MAX; ++i) A[i] = true;
    for (int i = 2; i < MAX; ++i) {
        if (!A[i]) continue;
        if (i >= x) {
            cout << i << endl;
            break;
        }
        int a = i * 2;
        while (a < MAX) {
            A[a] = false;
            a += i;
        }
    }
    return 0;
}