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<sstream>
#include<vector>
#include<iterator>
#include<algorithm>
using namespace std;

vector<int> generatePrime(int n) {
    vector<int> prime;
    vector<bool> v(n + 1, true);
    v[0] = false;
    v[1] = false;

    for (int i = 2; i < (int)v.size(); i++) {
        if (v[i] == false)
            continue;

        prime.push_back(i);
        for (int j = i + i; j < (int)v.size(); j += i)
            v[j] = false;
    }

    return prime;
}

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

    vector<int> prime = generatePrime(X * 2);
    int ans = *lower_bound(prime.begin(), prime.end(), X);
    
    cout << ans << endl;

    return 0;
}