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>
#define MAX 100000010

int P[MAX] = {0};

int main()
{
    int i, j;
    for (i=2; i<MAX; i++) {
        if (P[i] == 0) {
            for (j=2*i; j<MAX; j+=i) {
                P[j] = 1;
            }
        }
    }
    
    int count = 0;
    int N;
    scanf("%d", &N);
    for (i=0; i<N; i++) {
        int a;
        scanf("%d", &a);
        if (P[a] == 0) {
            count++;
        }
    }    
    
    printf("%d\n", count);
    
    return 0;
}