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.to_i

cnt = Hash.new(0)
gets.split.map(&:to_i).sort.each do |a|
  cnt[a] += 1
end

a = cnt.keys
a.each do |ai|
  cnt.delete(ai) if cnt[ai] > 1
end

i = 0
n = a.size
while i < n do
  (i+1...n).each do |j|
    cnt.delete(a[j]) if a[j] % a[i] == 0
  end
  a = cnt.keys
  n = a.size
  i += 1
end
p cnt.values.sum