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 {

	static boolean[] prime;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		prime = new boolean[100000001];
		int count = 0;

		for (int i=2; i<=10000; i++) {
			if (prime[i]) continue;
			for (int j=i*2; j<=100000000; j+=i) {
				prime[j] = true;
			}
		}

		int n = sc.nextInt();
		for (int i=0; i<n; i++) {
			int num = sc.nextInt();
			if (!prime[num]) {
				count++;
			}
		}

		System.out.println(count);

		sc.close();
	}

}