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: Time Limit Exceeded)

input = defined?(DATA) ? DATA : STDIN

_ = input.gets.to_i
list = input.gets.split(' ').map(&:to_i).sort

hash = {}
list.each do |a|
  if hash[a].nil?
    hash[a] = true
  else
    hash[a] = false
  end
end

list2 = hash.keys
status = hash.values

list2.each_with_index do |a, i|
  next if status[i].nil?
  a_x2 = a * 2
  ((i + 1)...list2.size).each do |j|
    next unless status[j]
    b = list2[j]
    next if b < a_x2
    if b % a == 0
      status[j] = nil
    end
  end
end

puts status.count { |s| s }