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 PHP (judge verdict: Accepted)

<?php

class Solver
{
    private $number_of_elements;
    private $nature_numbers = array();

    public function __construct()
    {
        $lines = array();
        while (1) {
            if (!$line = fgets(STDIN)) break;
            $line = trim($line);
            $lines[] = $line;
        }

        $this->number_of_elements = $lines[0];
        $this->nature_numbers = array_slice($lines, 1);
    }

    public function getAnswer()
    {
        $counter = 0;
        foreach ($this->nature_numbers as $nature_number) {
            $counter += $this->isPrimeNumber($nature_number) ? 1 : 0;
        }
        echo $counter, PHP_EOL;
    }

    public function isPrimeNumber($n)
    {
        if ($n == 2) return true;
        elseif ($n % 2 == 0) return false;

        $sqrt_n = sqrt($n);
        for ($i = 3; $i <= $sqrt_n; $i += 2) {
            if ($n % $i == 0) return false;
        }
        return true;
    }
}

$answer = new Solver;
$answer->getAnswer();