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 PartialTypeSignatures #-}
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE MultiWayIf #-}
module Main (main) where
-- module ABC.ABC170.D where

import qualified Data.ByteString.Char8 as C8
import qualified Data.Char as C
import qualified Data.List as L
import Data.Vector.Unboxed (Vector)
import qualified Data.Vector.Unboxed as V
import qualified Data.Vector.Unboxed.Mutable as MV
import qualified Data.Vector.Generic.Mutable as MGV
import qualified Data.Vector.Algorithms.Merge as V
import Control.Monad.ST
import Control.Monad

main :: IO ()
main = do
  [n] <- readInts
  readIntsV >>= output . solve n

solve :: Int -> Vector Int -> Int
solve n vec = V.sum $ runST $ do
  mvec <- V.thaw vec
  V.sort mvec
  forM_ [0..n-1] $ \i -> do
    x <- MV.unsafeRead mvec i
    when (x > 0) $ do
      MV.write mvec i 1
      forM_ [i+1..n-1] $ \j -> do
        y <- MV.unsafeRead mvec j
        when (y > 0) $ do
          when (x==y) $ MV.write mvec i 0
          when (y `mod` x == 0) $ MV.write mvec j 0
  V.unsafeFreeze mvec

output :: Int -> IO ()
output = print

-- utils
readInts :: IO [Int]
readInts = L.unfoldr (C8.readInt . C8.dropWhile C.isSpace) <$> C8.getLine

readIntsV :: IO (Vector Int)
readIntsV = V.unfoldr (C8.readInt . C8.dropWhile C.isSpace) <$> C8.getLine