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.util.Scanner

fun main(args: Array<String>) {
    try {
        val sc = Scanner(System.`in`)
        val n = sc.nextInt()
        var c = 0
        for (i in 0 until n) {
            val a = sc.nextInt()
            if (a < 2 || a > 100_000_000) {
                throw Exception("Illegal input.")
            }
            if (isPrimeFast(a)) c++
        }
        println(c)
    } catch (e: Exception) {
        println(e)
    }
}

fun isPrimeFast(a: Int): Boolean {
    val p = Math.sqrt(a.toDouble()).toInt()
    for (i in 2..p) {
        if (a % i == 0) {
            return false
        }
    }
    return true
}

fun isPrimeSlow(a: Int): Boolean {
    for (i in 2..a) {
        if (a % i == 0) {
            return false
        }
    }
    return true
}