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)

require 'prime'

def divisors(n)
  n.prime_division.inject([1]) do |ary, (p, e)|
    (0..e).map{ |e1| p ** e1 }.product(ary).map{ |a, b| a * b }
  end.sort
end

N = gets.to_i
A = gets.chomp.split(" ").map(&:to_i).sort

ans = 0
(0...N).each{|i|
  next if i > 0 && A[i] == A[i-1]
  next if i < N-1 && A[i] == A[i+1]
  f = true
  divisors(A[i]).each{|d|
    idx = A[0, i].bsearch_index{|x| x >= d}
    next if idx.nil?
    (f = false; break) if d == A[idx]
  }
  ans += 1 if f
}

puts ans