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 OCaml (judge verdict: Accepted)

let prime_p = function
  | 2 -> true
  | n when n < 2 || n mod 2 = 0 -> false
  | n ->
      let rec doit i =
        if i*i > n then true
        else if n mod i = 0 then false
        else doit (i + 2)
      in
      doit 3

let () =
  let n = read_int () in
  let rec read i cnt =
    if i >= n then cnt
    else read (i + 1) (cnt + (if prime_p (read_int ()) then 1 else 0))
  in
  Printf.printf "%d\n" (read 0 0)