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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;

int main()
{
	int x,i,j,k=0,a,b;
	cin>>x;
	stack<int> s,r;
	s.push(2);
	for(a=3;a<=x;a++)
	{
		k=0;
		r=s;
		b=r.size();
		for(i=0;i<b;i++)
		{
			j=r.top();
			r.pop();
			if(a%j==0)
			{
				k=1;
				break;
			}
		}
		if(k==0) s.push(a);
	}
	if(x==s.top()) cout<<x;
	else 
	{
		for(a=x+1;a>x;a++)
		{
			k=0;
			r=s;
			b=r.size();
		for(i=0;i<b;i++)
		{
			j=r.top();
			r.pop();
			if(a%j==0)
			{
				k=1;
				break;
			}
		}
		if(k==0)
		{
			cout<<a;
			break;
		}
		}
	}
	return 0;
}