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>

//素数であるかどうかを判定する
int PrimeNumbers(int num);

int main(void)
{
	int n;		//整数の個数
	int num;	//整数
	int cnt;	//素数の個数
	int i;

	//データの数を入力する
	scanf("%d", &n);

	cnt = 0;
	//整数を入力し、素数の数を数える
	for (i = 0; i < n; i++)
	{
		//整数を入力する
		scanf("%d", &num);

		if ((num % 2 != 0) || (num == 2))
		{
			//素数を判定する
			if (PrimeNumbers(num) == 1)
			{
				cnt++;
			}
			else
			{
				//処理をしない
			}
		}
		else
		{
			//処理をしない
		}
	}

	//結果を出力する
	printf("%d\n", cnt);

	return 0;
}

//素数であるかどうかを判定する
int PrimeNumbers(int num)
{
	int i;

	//素数は2からなので初期値を2にして素数を調べる
	for (i = 2; i <= num; i++)
	{
		if ((num % i == 0) && (i == num))
		{
			return 1;
		}
		else if((num % i == 0) && (i != num))
		{
			return 0;
		}
		else
		{
			//処理をしない
		}
	}
}