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)

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

function main()
  n = readline() |> parseInt
  a = zeros(Int, n)
  a = readline() |> split |> parseArray

  b = falses(10^6)
  for i in 1:n
    b[a[i]] = true
  end
  for i in 1:10^6
    b[i] || continue
    for j in 2i:i:(10^6 ÷ i) * i
      b[j] = false
    end
  end
  sort!(a)
  for i in 1:n
    i > 1 && a[i] == a[i - 1] && (b[a[i]] = false)
  end
  ans = count(b)

  println(ans)
end

main()