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"

func main() {
	var n int
	fmt.Scan(&n)
	a := make([]int, n)
	m := make(map[int]int)
	for i := 0; i < n; i++ {
		fmt.Scan(&a[i])
		m[a[i]]++
	}
	ans := 0
	for _, e := range a {
		found := true
		if v, ok := m[e]; ok && v > 1 {
			found = false
		}
		for i := 2; i*i <= e; i++ {
			if e%i == 0 {
				if v, ok := m[i]; ok && v >= 1 {
					found = false
					break
				}
				if v, ok := m[e/i]; i != e/i && ok && v >= 1 {
					found = false
					break
				}
			}
		}
		if found {
			ans++
		}
	}
	fmt.Println(ans)
}