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<stdbool.h>
#include<math.h>
#define ll long long

bool sosuu(ll n){
  for(int i=3;i<sqrt(n);i+=2){
    if(n%i==0){
      return false;
    }
  }
  return true;
}

int main(){
  ll x,i;
  scanf("%lld",&x);
  if(x==2){
    printf("2");
    return 0;
  }
  if(x%2==0)x+=1;
  while(1){
    if(sosuu(x)) break;
    x+=2;
  }
  printf("%lld",x);
  return 0;
}