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 {
	public static void main(String[] args){
		Scanner scan=new Scanner(System.in);
		boolean[] prime=new boolean[(int)Math.pow(10,8)+1];
		prime[0]=prime[1]=true;
		int limit=(int)Math.pow(10,8);
		int limit2=(int)Math.sqrt(Math.pow(10,8));
		for(int i=2;i<limit2;){
			for(int j=2;i*j<=limit;j++){
				prime[i*j]=true;
			}
			for(int j=i+1;j<=limit;j++){
				if(!prime[j]){
					i=j;
					break;
				}
			}
		}
		int N=scan.nextInt();
		int count=0;
		for(int i=0;i<N;i++){
			if(!prime[scan.nextInt()]) count++;
		}
		System.out.println(count);
		scan.close();
	}
}