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 (Clang 3.8.0) (judge verdict: Accepted)

#include <iostream>
#include <cmath>
#include <vector>
#include <string>
#include <algorithm>
using namespace std;

#define FOR(i, a, b) for(int i = (a); i < (b); i++)
#define REP(i, n)  FOR(i, 0, n)
#define ASC(c) sort((c).begin(), (c).end())
#define DESC(c) sort((c).begin(), (c).end(), greater<int>())

#define DUMP(x)  cerr << #x << " = " << (x) << endl;
#define DEBUG(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;

typedef long long ll;
typedef unsigned long long ull;
struct edge { int u, v; ll w; };
 
ll MOD = 1000000007;
ll _MOD = 1000000009;
double EPS = 1e-10;

bool prime(int a) {
    if (a <= 1) return false;
    for (int i = 2; i * i <= a; i++)
        if (a % i == 0) return false;
    return true;
}

int main() {
    int x; cin >> x;
    while (!prime(x)) x++;
    cout << x << endl;
}