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 int MAX_COUNT= 100000000;
    public static void main(String[] args){
 
        boolean[] isPrimeNumber = createIsPrimeNumber();
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int count = 0;
        for(int i = 0; i <N; i++){
            int temp= sc.nextInt();
            if(isPrimeNumber[temp - 1]){
                count++;
            }
        }
        sc.close();
        System.out.println(count);
    }
     
    public static boolean[] createIsPrimeNumber(){
        boolean[] isPrimeNumber = new boolean[MAX_COUNT];
        for(int i = 0; i <MAX_COUNT; i++){
            isPrimeNumber[i] = true;
        }
        isPrimeNumber[0] = false;
        for(int i = 2; i < MAX_COUNT; i++){
            if(isPrimeNumber[i - 1]){
                int count = 2;
                while(true){
                    if((i * count - 1) >= MAX_COUNT ){
                        break;
                    }
                    isPrimeNumber[i * count - 1] = false;
                    count++;
                }
            }
        }
        return isPrimeNumber;
    }
}