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 = length . parse $ sort s

parse :: [Int] -> [Int]
parse s@(s1:s2:ss)
  | s1 == s2  = t
  | otherwise = s1:t
  where
    t = parse . filter ((/= 0) . (`mod` s1)) $ s

parse (s:ss) = s:(parse . filter ((/= 0) . (`mod` s)) $ ss)
parse [] = []