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 Ruby (2.7.1) (judge verdict: Wrong Answer)

require 'prime'

n = gets.to_i
a = gets.split.map(&:to_i).sort

x = Array.new(a[-1] + 1)
ans = 0

n.times do |i|
    if a[i] == a[i-1] || (i < n-1 && a[i] == a[i+1])
        next if x[a[i]]
        a[i].step(a[-1], a[i]) {|j| x[j] = true}
        next
    end

    next if x[a[i]]

    ans += 1

    a[i].step(a[-1], a[i]) {|j| x[j] = true}
end

p ans