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.chomp.to_i
array = gets.chomp.split.map(&:to_i)

hash = array.group_by(&:itself).map{ |key, value| [key, value.count] }.to_h

ng = {}

new_arr = []
hash.each do |k,v|
  if v == 1
    new_arr.push(k)
  else
    ng[k] = true
    new_arr.push(k)
  end
end

new_arr.sort!

new_n = new_arr.size

ans = 0
new_n.times do |i|
  next if ng[new_arr[i]]

  if Prime.prime?(new_arr[i])
    ans += 1
    next
  end

  next_flag = false
  i.times do |j|
    if new_arr[i] % new_arr[j] == 0
      next_flag = true
      break
    end

    if new_arr[j] > new_arr[i]/2
      next_flag = true
      ans += 1
      break
    end
  end
  next if next_flag
  ans += 1
end

p ans