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: Time Limit Exceeded)

module Main where

import Debug.Trace
import Data.List

main :: IO ()
main = do
  getLine
  s <- map read . words <$> getLine 
  --a `traceShow`
  print $ solve s

solve :: [Int] -> Int
--solve s = (\a -> a `traceShow` length a). parse mx . group $ s'
solve s = length . parse mx . group $ s'
  where
    s' = sort s
    mx = last s'

parse :: Int -> [[Int]] -> [Int]
parse mx (s:ss)
  | length s > 1 = parse mx t
  | otherwise = s':(parse mx t)
  where
    t = if mx `div` s' == 0 then ss else (filter ((/= 0) . (`mod` s') . head) $ ss)
    s' = head s

parse _ [] = []