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: Wrong Answer)

package main

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

const MaxA = 1_000_000

func main() {
	sc := NewScanner()

	n := sc.ReadInt()
	as := make([]int, n)
	for i := 0; i < n; i++ {
		as[i] = sc.ReadInt()
	}
	sort.Ints(as)

	count := 0
	sieve := make([]bool, MaxA+1)
	for _, a := range as {
		if !sieve[a] {
			count++
			for j := a; j <= MaxA; j += a {
				sieve[j] = true
			}
		}
	}

	fmt.Println(count)
}

// from [my library](https://github.com/ikngtty/go-contestlib)
// -   math/simple

func Abs(x int) int {
	if x >= 0 {
		return x
	}
	return -x
}

func Min(values ...int) int {
	if len(values) == 0 {
		panic("no values")
	}

	min := values[0]
	for _, v := range values {
		if v < min {
			min = v
		}
	}
	return min
}

func Max(values ...int) int {
	if len(values) == 0 {
		panic("no values")
	}

	max := values[0]
	for _, v := range values {
		if v > max {
			max = v
		}
	}
	return max
}

func Pow(base, exponent int) int {
	if exponent < 0 {
		panic(fmt.Sprintf("exponent (%d) should not be a minus", exponent))
	}

	answer := 1
	for i := 0; i < exponent; i++ {
		answer *= base
	}
	return answer
}

func Ceil(divident, dividor int) int {
	if dividor == 0 {
		panic("dividor should not be 0")
	}

	quo := divident / dividor
	rem := divident % dividor

	if rem != 0 {
		if (divident > 0 && dividor > 0) ||
			(divident < 0 && dividor < 0) {
			return quo + 1
		}
	}
	return quo
}

// -   sortutil

func ReverseInts(a []int) {
	sort.Sort(sort.Reverse(sort.IntSlice(a)))
}

func ReverseStrings(a []string) {
	sort.Sort(sort.Reverse(sort.StringSlice(a)))
}

// -   io

type Scanner struct {
	bufScanner *bufio.Scanner
}

func NewScanner() *Scanner {
	bufSc := bufio.NewScanner(os.Stdin)
	bufSc.Split(bufio.ScanWords)
	bufSc.Buffer(nil, 100000000)
	return &Scanner{bufSc}
}

func (sc *Scanner) ReadString() string {
	bufSc := sc.bufScanner
	bufSc.Scan()
	return bufSc.Text()
}

func (sc *Scanner) ReadInt() int {
	bufSc := sc.bufScanner
	bufSc.Scan()
	text := bufSc.Text()

	num, err := strconv.Atoi(text)
	if err != nil {
		panic(err)
	}
	return num
}