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: Memory Limit Exceeded)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;

public class Main{
    public static void main(String[] args) throws Exception{
        int number,count=0;
        double comp;
        boolean isPrime;
        ArrayList<Integer> prime = new ArrayList<>();
        ArrayList<Integer> exist = new ArrayList<>();
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String line = br.readLine();
        int n = Integer.parseInt(line);
        for(int i = 0; i<n ; i++) {
            line = br.readLine();
            exist.add(Integer.parseInt(line));
        }
        Collections.sort(exist);
        number = exist.get(exist.size()-1);

        if(number >= 2){
            prime.add(2);
        }

        for (int i = 3; i <= number; i += 2) {
            isPrime = true;
            for (int p : prime) {
                comp = (double) i / (double) p;
                if (p == 1) {
                    continue;
                }
                if (i % p == 0) { //iが見つかった素数で割り切れる
                    isPrime = false;
                    break;
                } else if (p > comp) {
                    break;
                }
            }
            if (isPrime) {
                prime.add(i);
            }
        }
        for( int e : exist){
            if(prime.contains(e)){
                count++;
            }
        }
        System.out.println(count);
    }
}