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: Memory Limit Exceeded)

#include<stdio.h>
long long a[100000000];
int main()
{
  long long i,j,s=0,c,n;
  a[1]=1;
  for(i=4;i<=100000000;i=i+2)
  {
    a[i]=1;
  }
  for(i=3;i*i<=100000000;i+=2)
  {
    if(a[i]!=1){
    for(j=i*i;j<=100000000;j=j+2*i)
    {
      a[j]=1;
    }
    }
  }
  scanf("%lld",&n);
  while(n--)
  {
    scanf("%lld",&c);
    if(a[c]==0) s++;
  }
  printf("%lld\n",s);
  return 0;

}