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 Lua (LuaJIT 2.1.0) (judge verdict: Wrong Answer)

local read = io.read
local insert = table.insert
local N = read("*n")
local A = {}
local has_A_s = {}

for i = 1, N do
	local num = read("*n")
	if has_A_s[num] == nil then
		has_A_s[num] = true
		insert(A, num)
	end
end

local count = 0
for i = 1, #A do
	for j = 1, #A do
		if i == j then
		elseif A[i] % A[j] == 0 then
			count = count + 1
			break
		end
	end
end

print((#A == 1) and 0 or #A - count)