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>
#include <string.h>
#include <stdlib.h>
#define MAX (int)1e8

void Prime(int *a)
{
  int i, j;
  for(i=2; i<MAX; i++){
    for(j=2; j*j<=i; j++){
      if(a[j] && i % j == 0) break;
    }
    if(j*j > i) a[i]=1;
  }
  return;
}

int main()
{
  int n, a=0, i, num;
  int *p = (int *)malloc(sizeof(int)*MAX);
  memset(p, 0, sizeof(int) * MAX);
  Prime(p);
  scanf("%d", &n);
  for(i=0; i<n; i++){
    scanf("%d", &num);
    if(p[num]) a++;
  }
  printf("%d\n", a);
  return 0;
}