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 (
	"fmt"
	"sort"
	"math"
)

func main() {
	var n int
	fmt.Scanf("%d", &n)
	a := make([]int, 0, n)
	m := map[int]int{}

	for i := 0; i < n; i++ {
		var tmp int
		fmt.Scanf("%d", &tmp)
		m[tmp]++
		if (m[tmp] <= 2) {
			a = append(a, tmp)
		}
	}
	sort.Ints(a)
	// fmt.Printf("%v\n", a)

	count := 0
	for i := 0; i < len(a); i++ {
		flag := true
		sqrt := int(math.Sqrt(float64(a[i])))
		for j := 0; j < len(a); j++ {
			if (i == j) {
				continue
			}
			if (a[j] > sqrt + 1) {
				break
			}
			if ((a[i] % a[j]) == 0) {
				flag = false
				break
			}
		}
		// 自分の前後の要素が重複要素かもしれない
		if (i > 0) && (a[i] % a[i-1]) == 0 {
			flag = false
		}
		if (i < len(a) -1) && (a[i] % a[i+1]) == 0 {
			flag = false
		}
		if (flag) {
			count++
		}
	}

	fmt.Printf("%d", count)
}