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: Time Limit Exceeded)

$primes = Array.new(0);

def array_integer(a)
	0.upto(a.count) {|x|
		a[x] = a[x].to_i
	}
	return a
end

def is_prime(num)
#	print "prime check for ", num , "\n"
	return true if num == 2
	return false if num < 2
	return false if num % 2 == 0
	return true if $primes.find{|i| i == num} != nil
#	print $primes.length, "\n"
	if $primes.length > 0 then
#		p $primes
		0.upto($primes.length - 1) {|i|
			break if num < $primes[i]
			return false if num % $primes[i] == 0
		}
 #   	print "prime list miss\n"
		test_num = $primes[$primes.length - 1]
	else
		test_num = 3
	end	
	while num / 2 > test_num do
		if is_prime(test_num) then
			return false if num % test_num == 0
		end
		test_num += 2
	end
	$primes.push(num) if $primes.find{|i| i == num} == nil
#	print "prime check end for ", num , "\n"
	return true
end


n = STDIN.gets.chomp.to_i
count = 0

1.upto(n) {
	num = STDIN.gets.chomp.to_i
    if is_prime(num) then 
	    count += 1 
    end
}
print count, "\n"