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 Haskell (GHC 8.8.3) (judge verdict: Wrong Answer)

import Data.List

main = interact $ show . sol . map read . tail . words

sol as = length $ f mx as'
  where
  as' = sort as
  mx = last as'

f _ [] = []
f mx (a:as) = if a `elem` as 
    then f mx' as'
    else if a*2>mx 
      then a:as
      else a:f mx' as'
  where
  as' = filter ((>0) . (`rem` a)) as
  mx' = last as'