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)

include Math
require 'prime'

n = gets.to_i
root_prime = Prime.each(10000).to_a
c = 0

n.times {
  x = gets.to_i
  if (x <= 10000)
    c += 1 if (root_prime.include?(x))
    next
  end
  xs = sqrt(x).floor
  root_prime.each{ |rp|
    if (rp > xs)
      c += 1
      break
    end
    break if (x % rp == 0)
    c += 1 if (rp == root_prime.last) && (xs > rp)
  }
}
puts c