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: Runtime Error)

#include<stdio.h>
#define MAX 9999999999
int main(void){
  long long int n,i,a[MAX],j;
  scanf("%lld",&n);
  for(i=0;i<MAX;i++){
    a[i]=0;
  }
  a[0]=1;
  for(i=2;i<MAX/2;i++){
    for(j=2;i*j<=MAX;j++){
      if(a[i*j-1]==0) a[i*j-1]=1;
    }
  }
  for(i=0;i<MAX;i++){
    if(a[i]==0&&i+1>=n){
      printf("%lld",i+1); 
      return 0;
    }
  }
  return 0;
}