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 <math.h>
#include <string.h>
#include <stdlib.h>

void sieve(int *list, long max) {
  int i,j;
  list[0] = 1;
  list[1] = 1;
  for(i = 2; i <= (int)sqrt(max); i++) {
    if(list[i] == 0) {
      for(j = 2; i*(long)j <= max; j++) list[i*j] = 1;
    }
  }
}


int main() {
  int N,i,t;
  scanf("%d", &N);
  long a[N],max;
  max = 0;
  for(i = 0; i < N; i++) {
    scanf("%ld", a+i);
    if(a[i] > max) max = a[i];
  }
  int *prime_list;
  prime_list = (int *)malloc(sizeof(int) * (max+1));
  memset(prime_list, 0, sizeof(int) * (max+1));
  sieve(prime_list,max);

  t = 0;
  for(i = 0; i < N; i++) {
    if(prime_list[a[i]] == 0) t++;
  }
  printf("%d\n", t);
  
  return 0;
}