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 Julia (1.4.0) (judge verdict: Wrong Answer)

parseInt(x)=parse(Int, x)
parseMap(x::Array{SubString{String},1})=map(parseInt, x)

function main()
	n = readline() |> parseInt
	a = readline() |> split |> parseMap |> sort
	c = zeros(Int,10^6)
	ans = 0
	for i in 1:n
		x = 2
		f = 0
		while x*x<a[i]
			if a[i]%x==0
				if c[x]==1||c[div(a[i],x)]==1
					f = 1
					break
				end
			end
			x += 1
		end
		if x*x==a[i]&&c[x]==1
			f = 1
		end
		if f == 0
			ans += 1
		end
		c[a[i]]+=1
	end
	println(ans)
end

main()