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: Accepted)

import java.io.*
import java.util.*
import kotlin.math.*

fun main(){
	val f = BufferedReader(InputStreamReader(System.`in`))

	val n = f.readLine().toInt()
	val array = f.readLine().split(" ").map{it.toInt()}.toIntArray().sorted()

	val MAXA = 1000005
	val remaining = BooleanArray(MAXA){true}

	var answer = 0
	for(k in 0 until n){
		if(remaining[array[k]] && !(k < n-1 && array[k+1] == array[k])) answer++
		if(k > 0 && array[k-1] == array[k]) continue
		for(j in array[k] until MAXA step array[k]) remaining[j] = false
	}

	println(answer)

}