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.*;

public class Main {
    public static void main(String[] args) {
    	Scanner sc = new Scanner(System.in);
        String line = sc.nextLine();
        int number = Integer.parseInt(line);
        int[] nature = new int[number];
        
        for(int i=0;i<number;i++){
        	nature[i]=Integer.parseInt(sc.nextLine());
        }       
        
        int[] half = new int[number];        
        
        for(int i=0;i<number;i++){
            if(nature[i]%2==0){
            	half[i]=nature[i]/2;
            }else{
            	half[i]=(nature[i]/2)+1;
            }
        }
        
        int count=0;

        for(int i=0;i<number;i++){
        	int fig=1;
        	if(nature[i]==2){
        		fig=1;
        	}else{
        	
        	for(int j=half[i];j>1;j--){      		
        		if(nature[i]%j==0){
        			fig=0;
        		}
        	}	
        	}
        	
        	if(fig==1){
        		count++;
        	}         	
        }
        
        System.out.println(count);
        
    }   
}