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 <stdio.h>
#include <stdlib.h>

int is_prime(int num, int *prime_nums, int size)
{
	int i;

	for(i = 0; i < size; i++) {
		if(num % prime_nums[i] == 0)
			return 0;
	}
	for(i = 2; i < num; i++) {
		if(num % i == 0)
			return 0;
	}
	prime_nums[size] = num;
	return 1;
}

int main(void) 
{
	int n, i, num, prime_num = 0;
	int *prime_nums;

	scanf("%d", &n);
	prime_nums = malloc(sizeof(int) * n);
	for(i = 0; i < n; i++) {
		scanf("%d", &num);
		prime_num += is_prime(num, prime_nums, prime_num);
	}
	printf("%d\n", prime_num);
	return 0;
}