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 <vector>
using namespace std;
int Sieve(int x){
    long long n = 100004;
    long long ans;
    vector<bool> flags(n, true);
    flags[0] = false;
    flags[1] = false;
    for(long long p = 2; p<n; ++p){
        if(!flags[p]) continue;
        for(long long mult = p * p; mult < n; mult += p)
            flags[mult] = false;
    }
    for(ans=x; ans<n; ++ans){
        if(flags[ans]) return ans;
    }
}
int main(){
    long long x,ans;
    cin >> x;
    ans = Sieve(x);
    cout << ans << "\n";
    return 0;
}