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: Accepted)

#include <stdio.h>

int main(void)
{
  int x, i;

  scanf("%d", &x);
  if(x == 2) {
    printf("%d\n", x);
  } else {
    if(x % 2 == 0) x++;
    
    for(;;) {
      for(i = 3; i < x; i += 2) {
	if(x % i == 0) break;
      }
      if(i == x) break;
      x++;
    }
    
    printf("%d\n", x);
  }
  return 0;
}