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 Scala (judge verdict: Accepted)

object Main {
  def main(args: Array[String]): Unit = {
    val n = io.StdIn.readInt()
    val count =
      Iterator.continually(io.StdIn.readInt())
        .take(n)
        .count(isPrime)
    println(count)
  }

  def isPrime(n: Int): Boolean = {
    val rt = Math.sqrt(n).toInt

    @annotation.tailrec
    def isPrime(i: Int): Boolean = {
      if (i <= rt)
        if (n % i ==0) false
        else isPrime(i + 2)
      else
        true
    }

    if (n == 2)
      true
    else if (n < 2 || n % 2 == 0)
      false
    else
      isPrime(3)
  }
}