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: Runtime Error)

package main

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

func main() {
	var n int
	var at []string
	var a []int
	fmt.Scan(&n)

	sc := bufio.NewScanner(os.Stdin)
	if sc.Scan() {
		at = strings.Split(sc.Text(), " ")
	}

	for _, e := range at {
		num, _ := strconv.Atoi(e)
		a = append(a, num)
	}

	sort.Sort(sort.Reverse(sort.IntSlice(a)))

	var count int

	if a[n-1] != a[n-2] {
		count = 1
	} else {
		count = 0
	}

	for i := 0; i < n; i++ {
		for j := i + 1; j < n; j++ {
			if a[i] == 0 || a[j] == 0 {
				break
			}
			if a[i]%a[j] == 0 {
				break
			}
			if i != 0 && a[i] == a[i-1] {
				break
			}
			if j == n-1 {
				count += 1
			}
		}
	}

	fmt.Print(count)

}