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 solution(n int, a []int) int {
        c := 0
        for i := range a {
                for j := range a {
                        if j > 1e3 {
                                break
                        }
                        if i != j {
                                if a[i]%a[j] == 0 {
                                        c++
                                        break
                                }
                        }
                }
        }
        return n - c
}

func main() {
        var n int
        fmt.Scan(&n)
        a := make([]int, n)
        for i := range a {
                fmt.Scan(&a[i])
        }
        fmt.Println(solution(n, a))
}