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: Wrong Answer)

var countPrimes = function(numbers) {
  var max = Math.max.apply(Math, numbers);
  var numList = {};
  numbers.forEach(function(n) {
    if (!numList[n]) {
      numList[n] = 0;
    }
    numList[n] += 1;
  });
  var counter = 0;
  var elems = [];
  for (var i = 3; i <= max; i += 2) {
    elems.push(i);
  }
  while (1) {
    var prime = elems.shift();
    counter += numList[prime] ? numList[prime] : 0;
    elems = elems.filter(function(elem) {
      return elem % prime !== 0;
    });
    if (prime > Math.sqrt(max)) {
      break;
    }
  }
  elems.forEach(function(elem) {
    counter += numList[elem] ? numList[elem] : 0;
  });
  return counter;
};

var input = require('fs').readFileSync('/dev/stdin', 'utf8');
var numbers = input.split('\n').map(Number);
numbers.shift();
console.log(countPrimes(numbers));