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 judge(int a);

int main()
{
  int X;
  int ans;
  
  scanf("%d",&X);
  
  if(X == 2){
    ans = 2;
  }
  else if(X%2 == 1){
    ans = judge(X);
  }
  else{
    ans = judge(X + 1);
  }

  printf("%d",ans);

  return 0;
}

int judge(int a){
  int i;

  for(i = 3;i < a;i += 2){
    if(a%i == 0){
      return judge(a + 2);
    }
  }

  return a;
}