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: Accepted)

n = gets.to_s.to_i
a = gets.to_s.split.map{|t|t.to_i}.sort

if n == 1 || (a[0] == 1 && a[1] != 1)
  puts 1
  exit
elsif a[0] == 1 && a[1] == 1
  puts 0
  exit
end

MAX_A = a[-1]
hantei = [true] * ( MAX_A + 1 )

a.each_with_index do |t, i|
  
  if hantei[t]
    
    hantei[t] = false if t == a[i+1]

    s = t + t
    while s <= MAX_A
      hantei[s] = false
      s += t
    end
  end
end

ans = 0
a.each do |t|
  ans += 1 if hantei[t]
end

puts ans