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>
#define N 100000001
int a[N] = {1, 1};
int main(){
    for(int i = 2; i <= sqrt(N); i++){
        if(a[i]==0){
            for(int j = i*i; j <= N; j+=i){
                a[j] = 1;
            }
        }
    }

    int n;
    int cnt = 0;
    scanf("%d", &n);
    while(n--){
        int b;
        scanf("%d", &b);
        if(a[b] == 0){
            cnt++;
        }
    }
    printf("%d\n", cnt);
    return 0;
}