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 'prime'

def _divisors(primes, k)
  Enumerator.new do |y|
    if primes.size == k
      y << 1
    else
      p, e = primes[k]
      _divisors(primes, k + 1).each {|d|
        (e + 1).times {|e1|
          y << p ** e1 * d
        }
      }
    end
  end
end

def divisors(n)
  _divisors(Prime.prime_division(n), 0).to_a.sort
end

n = gets.to_i
a = gets.split.map &:to_i
b = a.map{|i| divisors(i)}
r = 0
for i in 0...n
  aa = a.clone
  aa.delete_at i
  b[i].each do |d|
    if aa.index(d)
      r += 1
      break
    end
  end
end
p r