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 (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
)

var (
	scanner = bufio.NewScanner(os.Stdin)
	w       = bufio.NewWriter(os.Stdout)
)

func readInt() (read int) {
	scanner.Scan()
	read, err := strconv.Atoi(scanner.Text())
	if err != nil {
		panic(err)
	}
	return
}

func main() {
	scanner.Split(bufio.ScanWords)
	defer w.Flush()

	n := readInt()
	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i] = readInt()
	}

	sort.Ints(a)

	cnt := 0
	for i := 0; i < n; i++ {
		s := 0
		for j := 0; j < n && a[i] >= a[j]; j++ {
			if i != j {
				if a[i]%a[j] == 0 {
					s++
					break
				}
			}
		}
		if s == 0 {
			cnt++
		}
	}
	fmt.Println(cnt)
}