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"
	"flag"
	"fmt"
	"os"
	"sort"
	"strconv"
	"testing"
)

/*-----------Main-----------*/

func main() {
	n := readI()
	a := readIs(n)
	sort.Ints(a)
	del := make([]bool, n)

	for i := 0; i < n; i++ {
		if del[i] {
			continue
		}
		for j := i + 1; j < n; j++ {
			if del[j] {
				continue
			}
			if a[j] == a[i] {
				del[i], del[j] = true, true
			} else if a[j]%a[i] == 0 {
				del[j] = true
			}
		}
	}
	ans := 0
	for i := 0; i < n; i++ {
		if !del[i] {
			ans++
		}
	}
	fmt.Println(ans)
}

/*-----------Utilities-----------*/

var sc = bufio.NewScanner(os.Stdin)

func init() {
	testing.Init()
	if flag.Parse(); flag.Arg(0) == "debug" {
		debug()
	}
	const maxBuf = 200100
	var buf []byte = make([]byte, maxBuf)
	sc.Split(bufio.ScanWords)
	sc.Buffer(buf, maxBuf)
}

func debug() {
	testFile, err := os.Open("./test/sample-3.in")
	if err != nil {
		fmt.Println("Error : There is no testfile.")
		os.Exit(1)
	}
	sc = bufio.NewScanner(testFile)
}

func readS() string {
	sc.Scan()
	return sc.Text()
}

func readSs(a int) []string {
	b := make([]string, a)
	for i := 0; i < a; i++ {
		b[i] = readS()
	}
	return b
}

func readI() int {
	sc.Scan()
	r, _ := strconv.Atoi(sc.Text())
	return r
}

func readIs(a int) []int {
	b := make([]int, a)
	for i := 0; i < a; i++ {
		b[i] = readI()
	}
	return b
}

func readF() float64 {
	sc.Scan()
	r, _ := strconv.ParseFloat(sc.Text(), 64)
	return r
}

func readFs(a int) []float64 {
	b := make([]float64, a)
	for i := 0; i < a; i++ {
		b[i] = readF()
	}
	return b
}

func max(a []int) int {
	l := len(a)
	m := a[0]
	for i := 1; i < l; i++ {
		if a[i] > m {
			m = a[i]
		}
	}
	return m
}

func min(a []int) int {
	l := len(a)
	m := a[0]
	for i := 1; i < l; i++ {
		if a[i] < m {
			m = a[i]
		}
	}
	return m
}

func sortI(a []int) []int {
	sort.Ints(a)
	return a
}

func reverse(a []int) []int {
	l := len(a)
	r := make([]int, l)
	for i := 0; i < l; i++ {
		r[i] = a[l-i-1]
	}
	return r
}

func countI(a []int, b int) int {
	l := len(a)
	var c int
	for i := 0; i < l; i++ {
		if a[i] == b {
			c++
		}
	}
	return c
}