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 lli long long int
#define pb push_back

bool verify (lli a)
{
    if (a == 0 || a == 1)
    {
        return true ;
    }
    if (a == 2 || a == 3)
    {
        return true ;
    }
    if (a % 2 == 0)
    {
        return false ;
    }
    for (lli i = 3 , end = sqrt(a) ; i <= end; i += 2)
    {
        if(a % i == 0)
        {
            return false ;
        }
    }
 
    return true ;
} 
int main ()
{
    lli a ;
    cin >> a ;

    while (1)
    {
        if (verify(a))
        {
            cout << a << endl ;
            return 0 ;
        }

        a++;
    }

    return 0 ;
}