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

func main() {
	var n int
	fmt.Scan(&n)
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	as := make([]int, n)
	m := make(map[int]bool)
	dup := make(map[int]bool)
	for i := range as {
		sc.Scan()
		as[i], _ = strconv.Atoi(sc.Text())
		if _, ok := m[as[i]]; ok {
			dup[as[i]] = true
		}
		m[as[i]] = true
	}
	sort.Sort(sort.IntSlice(as))
	var sum int
	ms := make([]int, 1e6+1)
	for i := range as {
		num := as[i]
		if ms[num] == 1 {
			continue
		}
		if _, ok := dup[as[i]]; !ok {
			sum++
		}
		for j := num; j <= 1e6; j += num {
			ms[j] = 1
		}
	}
	fmt.Println(sum)
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}