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 Haskell (judge verdict: Time Limit Exceeded)

-- | Main entry point to the application.
module Main where

import Control.Applicative
import Control.Monad
import Data.List
import Debug.Trace
import Text.Printf

isPrime :: Int -> Bool
isPrime n = null [i | i <- takeWhile (\x -> x * x <= n) primes, n `rem` i == 0] where
    primes = 2:3:[x | i <- [1..], j <- [-1,1], let x = 6*i+j, isPrime x]

-- | The main entry point.
main :: IO ()
main = do
    _ <- getLine
    ns <- concatMap (fmap (read :: String -> Int) . words) . lines <$> getContents
    let primes = filter isPrime (nub ns)
    putStrLn . show $ length primes