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: Wrong Answer)

<?php

$n = trim(fgets(STDIN));

for ($i = 0; $i < $n; $i++) {
    $numbers[] = fgets(STDIN);
}

$count = 0;

for ($i = 0; $i < $n; $i++) {
    $num = (double) $numbers[$i];

    if ($num == 2) {
        $count += 1;
    } elseif ( $num < 2 or ($num % 2) == 0) {
    } else {
        $start = 3;
        while ($start <= sqrt($num) + 1) {
            if ($num % $start == 0) {
                break;
            }
            $start += 2;
        }
        $count += 1;
    }
}

echo $count . PHP_EOL;