Problem:
Score : 400 points

Problem Statement

Given is a number sequence A of length N.

Find the number of integers i \left(1 \leq i \leq N\right) with the following property:

For every integer j \left(1 \leq j \leq N\right) such that i \neq j , A_j does not divide A_i.

Constraints

All values in input are integers.

1 \leq N \leq 2 \times 10^5

1 \leq A_i \leq 10^6

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_N

Output

Print the answer.

Sample Input 1

5
24 11 8 3 16

Sample Output 1

3

The integers with the property are 2, 3, and 4.

Sample Input 2

4
5 5 5 5

Sample Output 2

0

Note that there can be multiple equal numbers.

Sample Input 3

10
33 18 45 28 8 19 89 86 2 4

Sample Output 3

5

Solution in Kotlin (1.3.71) (judge verdict: Time Limit Exceeded)

import java.io.BufferedReader
import java.io.InputStream
import java.io.InputStreamReader
import java.io.PrintWriter
import java.lang.StringBuilder
import java.util.*

fun PrintWriter.solve(sc: FastScanner) {
    val n = sc.nextInt()
    val a = Array(n) { sc.nextInt() }
    val count = mutableMapOf<Int, Int>()
    for (i in 0 until n) {
        count[a[i]] = (count[a[i]] ?: 0) + 1
    }
    val ok = BitSet(1000005)
    for (i in 0 until n) {
        ok[a[i]] = true
    }
    a.sort()
    var ans = 0
    for (i in 0 until n) {
        if (ok[a[i]] && count[a[i]]!! == 1) {
            ans++
        }
        var j = 2
        while (a[i] * j < 1000005) {
            ok[a[i] * j] = false
            j++
        }
    }
    println(ans)
}

fun main(args: Array<String>) {
    val writer = PrintWriter(System.out, false)
    writer.solve(FastScanner(System.`in`))
    writer.flush()
}

class FastScanner(s: InputStream) {
    private var st = StringTokenizer("")
    private val br = BufferedReader(InputStreamReader(s))

    fun next(): String {
        while (!st.hasMoreTokens()) st = StringTokenizer(br.readLine())

        return st.nextToken()
    }

    fun nextInt() = next().toInt()
    fun nextLong() = next().toLong()
    fun nextLine() = br.readLine()
    fun nextDouble() = next().toDouble()
    fun ready() = br.ready()
}