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>
#include <math.h>

int sosu(int s) {
  int i;
  double sq;
  if(s < 2) return 0;
  if(s == 2) return 1;
  if(s % 2 == 0) return 0;
  sq = sqrt(s);
  for(i = 3; i <= sq; i += 2) {
    if(s % i == 0) {
      return 0;
    }
  }
  return 1;
}

int main() {
  int x, z, z2;
  scanf("%d", &x);

  z2 = 2 * z;
  for(int z = x; 1; z++) {
    if(sosu(z)){
      printf("%d\n", z);
      return 0;
    }
  }
  return 0;
}