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 Kotlin (judge verdict: Accepted)

import java.lang.Math.sqrt

fun main(args: Array<String>) {
    val array = IntArray(readLine()?.toInt() ?: 0) {
        readLine()?.toInt() ?: 0
    }
    val primeJudge = PrimeJudge(array.max() ?: 0)
    println(array.filter(primeJudge::isPrime).count())
}

class PrimeJudge(max: Int) {
    private val numArray = BooleanArray(max+1) { true }
    init {
        numArray[0] = false
        numArray[1] = false
        for (i in 2..sqrt(numArray.size.toDouble()).toInt()) {
            if (numArray[i]) {
                for (j in i * 2 until numArray.size step i) {
                    numArray[j] = false
                }
            }
        }
    }
    fun isPrime(num: Int) = numArray[num]
}