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)

import scala.io.StdIn.readInt

object Main {
  val r = Array(2,3,5,7)

  def pow(x:Long, y:Long, z:Long):Long = {

    def multi(m:Long, n:Long) = { ( (m%z) * (n%z) ) % z }

    def pow2(m:Long, n:Long, odd:Long, b:Long):Long = {
      n match {
        case 0 => 1
        case 1 => multi(m, odd)
        case _ =>
          pow2(multi(m,m), n/2, (if(n%2==1) multi(odd, b) else odd), multi(b,b))
      }
    }
    pow2(x, y, 1, x)
  }

  def twoPow(d:Int,s:Int):(Int,Int) = {
    if(d%2 == 1) (d,s)
    else twoPow(d>>1,s+1)
  }

  def maybePrime(i:Int,d:Int,s:Int, n:Int):Boolean = {
    if(i>3) true
    else {
      val a = r(i)
      val x = pow(a,d,n)

      if(x==1 || x==n-1) maybePrime(i+1,d,s,n)
      else repeat(s-1,x*x%n, i, d, s, n)
    }
  }

  def repeat(j:Int, x:Long, i:Int, d:Int, s:Int, n:Int):Boolean = {
    if(j==0) false
    else if(x==1) false
    else if(x==n-1) maybePrime(i+1,d,s,n)
    else repeat(j-1,x*x%n,i,d,s,n)
  }

  def isPrime(n:Int):Boolean = {
    if(n<5000) (2 to Math.sqrt(n).toInt).forall(n%_ != 0)
    else if(n%2==0) false
    else {
      val (d,s) = twoPow(n-1,0)
      maybePrime(0,d,s,n)
    }
  }

  def main(args:Array[String]) = {
    val n = readInt
    println((0 until n).count{ _=> isPrime(readInt) })
  }
}