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)

import Control.Monad

primes :: Integral a => [a]
primes = 2 : [n | n <- [3..], all ((>0).rem n) $ takeWhile ((<=n).(^2)) primes]

primesIn :: Integral a => [a] -> [a]
primesIn ns = filter ((flip elem) primes') ns
  where maxn = maximum ns
        primes' = takeWhile (<=maxn) primes

main :: IO ()
main = do
  n <- readLn
  ns <- replicateM n readLn
  print $ length $ primesIn ns