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: Accepted)

const double = Float64
const int = Int64

parseint(x) = parse(int, x)
readint() = map(parseint, split(readline()))

const Nmax = 10^6

function main()
  N = readint()[1]
  A = readint()

  A = sort(A)
  kusi = Vector{Bool}(undef, Nmax)
  kusi .= false

  cout = 0
  for i in 1:N-1
    a = A[i]
    kusi[a] && continue
    
    a < A[i+1] && (cout += 1)
    for j in a:a:Nmax
      kusi[j]=true
    end
  end
  
  kusi[A[end]] || (cout += 1)
  println(cout)
  
end

main()