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 newScanner() *bufio.Scanner {
	scanner := bufio.NewScanner(os.Stdin)
	scanner.Split(bufio.ScanWords)
	return scanner
}

var sc = newScanner()

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

func scanInts(n int) []int {
	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i] = scanInt()
	}
	return a
}

func scanString() string {
	if sc.Scan() {
		return sc.Text()
	}
	panic(sc.Err())
}

func main() {
	n := scanInt()
	a := scanInts(n)
	answer := notDivisible(n, a)
	fmt.Println(answer)
}

func debug(a ...interface{}) {
	// fmt.Println(a...)
}

func notDivisible(n int, a []int) int {
	sort.Ints(a)
	prev := -1
	maxA := a[n-1]
	divisors := make([]int, maxA+1)
	for i := 0; i < n; i++ {
		if prev == a[i] {
			continue
		}
		for j := 1; a[i]*j <= maxA; j++ {
			divisors[a[i]*j]++
		}
	}
	debug(divisors)
	count := 0
	for i := 0; i < n; i++ {
		if divisors[a[i]] == 1 {
			count++
		}
	}
	return count
}

func min(x, y int) int {
	if x < y {
		return x
	}
	return y
}