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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"fmt"
)

func main() {
	var N int
	fmt.Scan(&N)
	a_lis := make([]int, N)
	for i := 0; i < N; i++ {
		var a int
		fmt.Scan(&a)
		a_lis[i] = a
	}

	cnt := make([]int, 1e6+5)
	for i := 0; i < N; i++ {
		x := a_lis[i]
		if cnt[x] != 0 {
			cnt[x] = 2
			continue
		}
		for j := x; j < len(cnt); j += x {
			cnt[j]++
		}
	}
	ans := 0
	for i := 0; i < N; i++ {
		if cnt[a_lis[i]] == 1 {
			ans++
		}
	}
	fmt.Println(ans)
}