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"
	"fmt"
	"os"
	"sort"
	"strconv"
)

func enumDivisors(n int) (res []int) {
	for i := 1; i*i <= n; i++ {
		if n%i == 0 {
			res = append(res, i)
			if n/i != i {
				res = append(res, n/i)
			}
		}
	}
	return
}
func lib_CountInt(values []int) map[int]int {
	m := map[int]int{}
	for _, value := range values {
		m[value]++
	}
	return m
}
func main() {
	scanner := bufio.NewScanner(os.Stdin)
	const initialBufSize = 4096
	const maxBufSize = 1000000
	scanner.Buffer(make([]byte, initialBufSize), maxBufSize)
	scanner.Split(bufio.ScanWords)
	var N int
	scanner.Scan()
	N, _ = strconv.Atoi(scanner.Text())
	A := make([]int, N)
	for i := 0; i < N; i++ {
		scanner.Scan()
		A[i], _ = strconv.Atoi(scanner.Text())
	}
	fmt.Println(solve(N, A))
}
func solve(N int, A []int) (cnt int) {
	sort.Ints(A)
	aCounts := lib_CountInt(A)
	for _, a := range A {
		if aCounts[a] != 1 {
			continue
		}
		valid := true
		for _, e := range enumDivisors(a) {
			if _, ok := aCounts[e]; ok && e != a {
				valid = false
				break
			}
		}
		if valid {
			cnt++
		}
	}
	return
}