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: Memory Limit Exceeded)

import java.io.BufferedReader
import java.io.InputStreamReader

fun eulerSieve(n: Int): Pair<IntArray, BooleanArray> {
    val isPrime = BooleanArray(n, { true })
    val primes = mutableListOf<Int>()

    isPrime[0] = false
    isPrime[1] = false

    for (i in 2 until n) {
        if (isPrime[i])
            primes.add(i)
        for (prime in primes) {
            if (i * prime >= n)
                break
            isPrime[i * prime] = false
            if (i % prime == 0)
                break
        }
    }

    return Pair(primes.toIntArray(), isPrime)
}

fun main(args: Array<String>) {
    val n = 100000050
    val isPrime = eulerSieve(n).second
    BufferedReader(InputStreamReader(System.`in`))
            .readText()
            .trim()
            .split(regex = """\s+""".toRegex())
            .map { it.toInt() }
            .drop(n = 1)
            .filter { isPrime[it] }
            .count()
            .let { println(it) }
}