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)

n = gets.strip.to_i
a = gets.strip.split(" ").map do |i|
  i.to_i
end

a_num={}

a_uniq = a.uniq.sort

a.each do |v|
  a_num[v] = a_num[v].nil? ? 1 : a_num[v]+=1
end

values=[]

a_num.each do |k,v|
  values.push(k)  if v==1
end
sum = n
sum=0
values = values.sort.reverse
values.each do |v|
  f = true
  a_uniq.each do |v1|
    if v%v1 ==0 && v!=v1
      f = false
      a_uniq.delete(v)
    elsif v<v1
      break
    end
  end
  sum +=1 if f
end

print sum