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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashMap;

public class Main {

    static HashMap<Integer, Boolean> map = new HashMap<Integer, Boolean>();
    
    /**
     * @param args
     * @throws IOException
     * @throws NumberFormatException
     */
    public static void main(String[] args) throws NumberFormatException,
            IOException {

        BufferedReader reader = new BufferedReader(new InputStreamReader(
                System.in));

        int len = Integer.parseInt(reader.readLine());

        int[] arr = new int[len];

        String line;

        for (int i = 0; i < len; i++) {
            line = reader.readLine();
            arr[i] = Integer.parseInt(line);
        }

        int resultCount = 0;
        for (int j = 0; j < arr.length; j++) {
            if (isPrime(arr[j])) {
                resultCount++;
            }
        }

        System.out.println(resultCount);

    }

    private static boolean isPrime(int value) {
        
        if(map.entrySet().contains(value)){
            return map.get(value);
        }
        
        for (int i = 2; i < value; i++) {
            if (value % i == 0) {
                map.put(value, false);
                return false;
            }
        }
        map.put(value, true);
        return true;
    }

}