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 Ruby (judge verdict: Accepted)

require 'prime'

$primes_u10000 = Prime.each(10000).to_a

def prime?(n)
	return n == $primes_u10000.bsearch{|x| n <= x} if n <= 10000

	# trial division
	limit = Math.sqrt(n).floor
	$primes_u10000.each do |d|
		break if limit < d
		return false if n % d == 0
	end

	return true
end

count = 0

gets.to_i.times do
	count += 1 if prime? gets.to_i
end

p count