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 JAVA (judge verdict: Accepted)


import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int x = scanner.nextInt();
		int sum = 0;
		for (int i = 0; i < x; i++) {
			int n = scanner.nextInt();
			if (isPrime(n)) {
				sum++;
			}
		}
		System.out.println(sum);
	}

	public static boolean isPrime(int i) {
		if (i == 2)
			return true;
		if (i % 2 == 0)
			return false;
		if (i < 8)
			return true;
		if (i % 3 == 0)
			return false;
		int k = 5;
		while (k * k <= i) {
			if (i % k == 0)
				return false;
			if (i % (k + 2) == 0)
				return false;
			k += 6;
		}
		return true;
	}
}