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: Accepted)

#include <stdio.h>
#include <math.h>
int gcd(x,y){
  if (y==0){
    return x;
  }else{
    return gcd(y,x%y);
  }
}

int main()
{
  int x,n,i,j,g;
  int count=0;
  scanf("%d",&n);
  for(i=0;i<n;i++){
    scanf("%d",&x);
    g=1;
    for(j=1;j<=sqrt(x);j++){
      int m=gcd(j,x);
      if (m>g){
        g=m;
        break;
      }
    }
    if (g==1){
      count++;
    }
  }

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

  return 0;
}