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: Time Limit Exceeded)

package main

import "fmt"

func main() {
	var n int
	fmt.Scan(&n)

	pl := make([]int, n)
	var p int
	for i := 0; i < n; i++ {
		fmt.Scan(&p)
		pl[i] = p
	}

	count := 0
	for i := 0; i < n; i++ {
		flag := true
		for j := 0; j < n; j++ {
			if i == j {
				continue
			}
			if pl[i]%pl[j] == 0 {
				flag = false
				continue
			}
		}
		if flag {
			count++
		}
	}
	fmt.Println(count)
}