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)


{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE BangPatterns #-}

module Main where

import Debug.Trace
import qualified Data.Map.Strict as Map

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

solve :: [Int] -> Int
solve s = length . filter (\ss -> (Map.findWithDefault 0 ss t) == 1) $ s
  where
    mx = (maximum s) + 1
    t = build mx Map.empty s

type Table = Map.Map Int Int

build :: Int -> Table -> [Int] -> Table
build mx t [] = t
build mx t (s:ss) = build mx t' ss
  where
    t' = if (Map.findWithDefault 0 s t) > 0 then Map.insertWith (+) s 1 t else foldr (\a tt -> Map.insertWith (+) a 1 tt) t [s, s*2 .. mx]