Problem:
Prime Numbers

A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.

Write a program which reads a list of N integers and prints the number of prime numbers in the list.

Input

The first line contains an integer N, the number of elements in the list.

N numbers are given in the following lines.

Output

Print the number of prime numbers in the given list.

Constraints

1 ≤ N ≤ 10000

2 ≤ an element of the list ≤ 108

Sample Input 1

5
2
3
4
5
6

Sample Output 1

3

Sample Input 2

11
7
8
9
10
11
12
13
14
15
16
17

Sample Output 2

4

Solution in C (judge verdict: Runtime Error)

#include<stdio.h>
#include<math.h>

#define N 1000000

int main(){
  int n, a, box[N], i, j, cnt=0;

  for(i=2; i<N; i++){
    box[i]=1;
  }
  
  for(i=3; i<N-1; i++){
    if(i%2==0){
      box[i]=0;
    }else{
      for(j=3; j<=sqrt(i); j+=2){
	if(i%j==0){
	  box[i]=0;
	  break;
	}
      }
    }
  }
  
  scanf("%d", &n);
  
  for(i=0; i<n; i++){
    scanf("%d", &a);
    if(box[a]==1){
      cnt++;
    }
  }

  printf("%d\n", cnt);

  return 0;
}