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: Accepted)

import Control.Monad (replicateM)
main = do
        n <- readLn
        nums <- replicateM n readLn
        print.length.filter isPrime $ nums

primes :: [Int]
primes = 2 : 3 : filter isPrime [5,7..]

isPrime :: Int -> Bool
isPrime n = ip n primes

ip n (p:ps)
    | p > sqrtn     = True
    | n `mod` p == 0 = False
    | otherwise      = ip n ps
    where sqrtn = floor.sqrt.fromIntegral $ n