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 = $stdin.gets.to_i
A = $stdin.gets.split.map {|i| i.to_i }
A.sort!
Am = {}
A.each do |a|
  Am[a] ||= 0
  Am[a] += 1
end
Ama = Am.to_a
AmaLen = Ama.length
if AmaLen == 1
  puts 0
  exit
end
#$stderr.puts Ama.to_s
cnt = 0
0.upto(AmaLen - 1) do |i|
  ai, ci = Ama[i]
  if ci > 1
    next
  end
  #$stderr.print "#{ai}:"
  inc = 1
  0.upto(i - 1) do |j|
    aj, = Ama[j]
    #$stderr.print " #{aj}[#{ai % aj}]"
    if ai % aj == 0
      inc = 0
      #$stderr.print " *"
      break
    end
  end
  #$stderr.puts
  cnt += inc
end
puts cnt