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: Time Limit Exceeded)

import java.util.Scanner;
public class Main{
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int counter = 0;
        int [] primes = new int[100000000];
        for(int x = 0; x < primes.length; x++){
            primes[x] = 0;
        }
        for(int x = 2; x < primes.length; x++){
            if(primes[x] == 0){
                for(int y = 2; y * x < primes.length;y++){
                    primes[y *x] = 1;
                }
            }
        }
        for(int x = 0; x < n; x++){
            int k = scan.nextInt();
            if(primes[k] == 0){
                counter++;
            }
        }
        System.out.println(counter);
    }
}