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<stdio.h>
#include<vector>
#include<algorithm>
#include<string.h>
#include<iostream>
#include<queue>
#include<stack>
#include<math.h>
#define Max 1000000
#define INF 1000000000000000000
using namespace std;

bool prime[Max];

void makePrime(){

	for(int i=0;i<Max;i++)
		prime[i] = true;
	for(int i=4;i<Max;i+=2)
		prime[i] = false;
	for(int i=3;i*i<Max;i++){
		if(prime[i]){
			for(int j=i*i;j<Max;j+=i)
				prime[j] = false;
		}
	}
}


int main(){

	makePrime();
	int x;
	scanf("%d",&x);
	while(prime[x] != true)
		x++;
	printf("%d\n",x);
	
	return 0;
}