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 is_prime n =
  if n = 2 || n = 3 || n = 5 then true
  else if n mod 2 = 0 || n mod 3 = 0 || n mod 5 = 0 then false
  else
    let rec loop i =
      if i*i > n then true
      else if n mod i = 0 then false
      else if n mod (i+2) = 0 then false
      else loop (i+6);
    in loop 5

let () =
  let n = read_int () in
  let rec read ct = function
      0 -> ct
    | i ->
       let m = read_int () in
       read (if is_prime m then ct+1 else ct) (i-1)
  in
  Printf.printf "%d\n" (read 0 n)