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

class Main{
    public static void main(String[] args) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        int cnt = 0;
        for(int i=0;i<n;i++){
            if(isPrime(Integer.parseInt(br.readLine())))cnt++;
        }
        System.out.println(cnt);
    }
    public static boolean isPrime(int x){
        if(x == 2)return true; // 2
        else if(x % 2 == 0)return false;
        else if(x <= 7)return true; // 3,5,7
        else if(x % 3 == 0)return false;

        for(int i=5; i*i<=x; i+=6){
            if(x % i == 0)return false;
            if(x % (i + 2) == 0)return false;
        }
        return true;
    }
}