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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <math.h>


int main(void){

    int X = 0;
    int d_X = 0.0;
    int flag = 0;

    scanf("%d", &X);

    d_X = sqrt((double)X);

    while (flag == 0){

        if (X % 2 == 0){
            X++;

        } else {

            for (int i = 3; i <= (int)d_X; i += 2){

                if (X % i == 0){
                    X++;
                    break;

                } else {
                    flag = 1;
                    break;
                }     
            }
        }

    }
    printf("%d", X);

    return 0;
}