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)

readnum(T::Type{<:Number} = Int) = parse.(T, split(readline()))
let
  ans = 1
  _ = readline()
  A = sort(unique(readnum()))
  N = length(A)
  N == 1 && (println(0); exit())
  for i = 2:N
    0 ∉ prod(A[i] .% A[1:i-1]) && (ans += 1)
  end
  println(ans)
end