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;
// #define int long long
mt19937 rnd(time(0));
typedef long long ll;
typedef long double ld;

// #define _GLIBCXX_DEBUG
#define f first
#define s second
#define pb push_back
#define pii pair<int, int> 
#define vi vector<int>
#define int ll

void solve(){
    int x;
    cin >> x;
    const int maxn = 2e5;
    bool p[maxn];
    memset(p, 0, sizeof(p));
    for (int i = 2; i < maxn; ++i) {
        if (p[i] == 0) {
            for (int j = 2 * i; j < maxn; j += i)
                p[j] = 1;
        }
    }
    while (p[x])
        x++;
    cout << x << endl;
}

signed main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    
    int t = 1;
    while(t--){
        solve();
    }
    
    return 0;
}