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: Time Limit Exceeded)

#include <iostream>

bool judge_prime(int num)
{
    if (num == 2 || num == 3) {
        return true;
    }

    for (int i = 2; i <= (num + 1) / 2; i++) {
        if (!judge_prime(i)){
              continue;
        }
        if (num % i == 0) {
            return false;
        }
    }
    return true;
}


int main()
{

    int num;
    std::cin >> num;

    int list[num];
    for (int i = 0; i < num; i++) {
        std::cin >> list[i];
    }

    int result = 0;
    for (int i = 0; i < num; i++) {
        if (judge_prime(list[i])) {
            result++;
        }
    }
    std::cout << result << std::endl;
}