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 'pp'

n = gets.to_i
a_n = gets.split.map(&:to_i)
group = a_n.group_by {|x| x}

#pp group
#p a_n

count = 0
a_n.each_with_index do |a, i|
    #pp "====="
    max = Math.sqrt(a).to_i
    tmp = a
    ok = true
    1.upto(max) do |n|
        #pp n
        if tmp % n == 0
            y = tmp / n
            #pp [n, y]
            if group[n]
                ok = false
                break
            end

            

            if group[y]
                if group[y].size != 1
                    ok = false
                    break
                elsif group[y][0] != a
                    ok = false
                    break
                end
            end
        end
    end

    if ok
        #pp i 
        count += 1
    end
end

pp count