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: Wrong Answer)

import java.io.*;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;
class Main{
    public static void main(String[] a){
        int first = 0;
        int last = 0;
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int num = 1;
        for (int w = 0; w < n; w++){
        first = scan.nextInt();
        if(first < 0){
        num = 0;}
        else if(first == 1){
        num = 0;
        } else if (first == 2){
        num = 1;
        } else if (first == 3){
        num = 1;
        }else{
        for(int i=3; i< first+1; i+=2){
        boolean prime = true;
        for(int div = 3; div <= Math.sqrt(i); div+=2){
        if(i%div == 0){
        prime = false;
        break;
        }
     }
     if(prime== true){
     num = num + 1;
     }
  }    
        }
      }
       System.out.println(num);
    }
     
}