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)

N = gets.to_i
ary = gets.split.map(&:to_i).sort.uniq
if ary.count == 1
  puts 0
else

    nums = Hash.new{|hash, key| hash[key] = 1 }
    ans = Array.new(ary.max + 1).map{|x| x = 0}
    result = 0
    
    ary.each do |i|
      nums[i]
    end
    
    ary.each do |j|
      ans[j] = 1
    end
    
    ary.each do |k|
      result += 1 if ans[k] == 1
      k.step(ary.max, k) do |l|
        ans[l] = 0
      end
    end
    puts result
end