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)

n = gets.chomp.to_i
a = gets.chomp.split(' ').map{|i| i.to_i }

i = 0
j = 0
count = 0
a.each{|ai|
  count += 1 unless a.any?{|aj|
    # p [count, i, j, ai, aj, ai > aj, ai % aj === 0, ai > aj && ai % aj === 0]
    j += 1
    if i === (j - 1)
      false
    else
      ai > aj && ai % aj === 0
    end
  }
  i += 1
}

puts count