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 <iostream>
#include <string>
#include <algorithm>
#include <iomanip>
#include <cmath>
#include <vector>
#include <set>
#include <bitset>
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
using lint = long long;
using namespace std;

const int MOD = 1000000007;

bool isPrime(int n) {
    int c = sqrt(n);

    if (n == 2 || n == 3 || n == 5) {
        return true;
    }

    for (int i = 2; i <= c+1; i++) {
        if (n % i == 0) return false;
    }
    return true;
}

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

    int s = X;
    while(!isPrime(s)) {
        s++;
    }
    cout << s << endl;
    return 0;
}