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)

/* Prime Numbers */

#include <stdio.h>
#define N 100000001

void sieve(int*,int);
int primep[N];

int main(void) {
  int n, x, count = 0, i;

  sieve(primep, N);
  scanf("%d", &n);

  for(i = 0; i < n; i++) {
    scanf("%d", &x);
    if(primep[x]) count++;
  }

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

  return 0;
}

void sieve(int* arr, int len) {
  int i,k;

  for(i = 0; i < len; i++) arr[i] = 1;
  arr[0] = arr[1] = 0;
  for(i = 0; i < len / 2; i++) {
    if(arr[i] == 0) continue;
    for(k = 2; i * k < len; k++)
      arr[i * k] = 0;
  }
}