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)

	A := make([]int, N)
	m := make(map[int]int)
	for i := range A {
		sc.Scan()
		A[i], _ = strconv.Atoi(sc.Text())
		m[A[i]]++
	}
	var keys []int
	for k := range m {
		keys = append(keys, k)
	}
	sort.Ints(keys)
	MAX := 1000000
	flags := make([]bool, MAX+1)
	for i := range flags {
		flags[i] = true
	}
	sum := 0
	for _, k := range keys {
		c := m[k]
		if !flags[k] {
			continue
		}
		if c == 1 {
			sum++
		}
		for num := k; num <= MAX; num += k {
			flags[num] = false
		}
	}
	fmt.Println(sum)

}