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.util.*
import java.lang.Math.*
import kotlin.collections.ArrayList

val readString: ()->String = {readLine()!!}
val readInt: ()->Int = {readLine()!!.toInt()}
val readLong: ()->Long = {readLine()!!.toLong()}
val readIntArray: ()->IntArray = {readLine()!!.split(' ').map{it.toInt()}.toIntArray()}
val readLongArray: ()->LongArray = {readLine()!!.split(' ').map{it.toLong()}.toLongArray()}
val errPrintln: (String)->Unit = {msg -> System.err.println(msg)}
val MOD = 1_000_000_007L
val INF = Int.MAX_VALUE/2
val LINF = Long.MAX_VALUE/2
data class IntPair(val first: Int, val second: Int)
data class To(val idx: Int, val cost: Long)


fun solve(A: IntArray): Int {
    val N = A.size
    if (N == 1) return 1

    when (A.count{it == 1}) {
        2-> { return 0 }
        1-> { return 1 }
        else -> {
            var B = A.sorted()
            if (B[0] == B.last()) return 0
            val hist = IntArray(1_000_002){0}

            for (i in 0 until N) {
                hist[B[i]] += 1
            }

            var res = ArrayList<Int>()

            while (B.isNotEmpty()) {
                if (hist[B[0]] == 1) {
                    res.add(B[0])
                }
                B = B.filter { it%B[0] != 0 }
            }

            return res.size
        }
    }
}


fun main(args: Array<String>) {
    val N = readInt()
    val A = readIntArray()

    val ans = solve(A)

    println(ans)
}