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,*A = $<.read.split.map(&:to_i)

n,as,bs = 0,A.sort,[]
until as.empty?
	a = as.shift
	n += 1 if a != as[0]
	until as.empty?
		ax = (as[0]+a-1)/a*a
		bs.push(*as.shift(as.index{|_|ax<=_}||as.size))
		as.shift(as.index{|_|ax<_}||as.size)
	end
	as,bs = bs,as
end
p n