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)

require 'set'

def main(str)
  as = str.split("\n")[1].split(" ").map(&:to_i).sort
  sets = Set.new
  nmax = 2 * 10 ** 5
  as.each.with_index.count do |a, i|
    next if sets.include?(a)
    x = a
    loop do
      sets << x
      x += a
      break if x > nmax
    end
    as[i + 1] != a
  end
end

unless ENV["TEST"]
  puts(main($stdin.read.chomp))
  exit(0)
end

require 'minitest/autorun'

class TestA < Minitest::Test
  def test_main
    assert_equal(3, main("5
24 11 8 3 16"))
    assert_equal(0, main("4
5 5 5 5"))
    assert_equal(5, main("10
33 18 45 28 8 19 89 86 2 4"))
  end
end