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 <stdio.h>
#define _USE_MATH_DEFINES
#include <math.h>
#include <set>
#include <string>
#include <vector>
#include <map>
#include <algorithm>
#include <cmath>
#include <limits>
#include <bitset>
#include <stack>
#include <queue>
#include <ctype.h>

typedef long long int lli;
#define rep(i,s,N) for(int i=s;i<N;i++)
#define MOD 1000000007
#define more(a,b) (((a)>(b))?(a):(b))
#define less(a,b) (((a)<(b))?(a):(b))

using namespace std;

int main(void)
{
	int X; cin >> X;
	if (X == 2) {
		cout << 2 << endl;
		return 0;
	}
	bool prime = true;
	while (true) {
		rep(i, 2, sqrt(X) + 1) {
			if (X%i == 0) {
				X++;
				prime = false;
				break;
			}
		}
		if (prime) {
			cout << X << endl;
			break;
		}
		else prime = true;
	}


	return 0;
}