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: Wrong Answer)

package main

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

var sc = bufio.NewScanner(os.Stdin)

func main() {
	sc.Split(bufio.ScanWords)
	n := nextInt()

	a := make([]int, n)
	var au []int
	var ad []int
	for i := 0; i < n; i++ {
		ai := nextInt()
		if !contain(au, ai) {
			au = append(au, ai)
		} else {
			ad = append(ad, ai)
		}
		a[i] = ai
	}
	sort.Slice(a, func(i, j int) bool { return a[i] < a[j] })
	sort.Slice(au, func(i, j int) bool { return au[i] < au[j] })

	max := au[len(au)-1]
	sieve := make([]bool, max)

	for k, _ := range sieve {
		sieve[k] = true
	}

	for _, a := range au {
		sieve = knit(sieve, a, max)
	}

	r := 0
	for _, ai := range a {
		if contain(ad, ai) {
			continue
		}
		if sieve[ai-1] == false {
			continue
		}
		r++
	}

	fmt.Println(r)
}

func knit(sieve []bool, n int, max int) []bool {
	i := 2
	t := n * 2
	for t < max {
		if sieve[t-1] == false {
			return sieve
		}
		sieve[t-1] = false
		i++
		t = n * i
	}

	return sieve
}

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func contain(h []int, n int) bool {
	for _, v := range h {
		if n == v {
			return true
		}
	}
	return false
}