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 JavaScript (judge verdict: Time Limit Exceeded)

(function(input) {
    var p = input.split('\n').map(Number);
    var n = p.shift();
    var a = p.slice(0, n);
    var max = Math.max.apply(null, a);
    var count = 0;
    for (var i = 1; i <= max; i++) {
        if (inArray(i, a) && isPrimeNumber(i)) {
            count++;
        }
    }
    console.log(count);
})(require('fs').readFileSync('/dev/stdin', 'utf8'));

function greatestCommonDevisor(x, y) {
    return Math.max.apply(null, commonDevisors(x, y));
}

function commonDevisors(x, y) {
    if (x > y) {
        x = x % y;
    } else if (x < y) {
        var tmp = y;
        y = x;
        x = tmp % x;
    }
    var a = [];
    var ds = divisors(x);
    for (var i = 0; i < ds.length ; i++) {
        var d = ds[i];
        if (y % d === 0) {
            a.push(i);
        }
    }
    return a;
}

function divisors(x) {
    var a = [];
    for (var i = 1; i <= x; i++) {
        if (x % i === 0) {
            a.push(i);
        }
    }
    return a;
}

function isPrimeNumber(x) {
    if (x < 2) {
        return false;
    }
    for (var i = 2; i < x; i++) {
        if (x % i === 0) {
            return false;
        }
    }
    return true;
}

function inArray(needle, heystack) {
    return heystack.indexOf(needle) !== -1;
}