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: Accepted)

{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE MultiWayIf #-}

import Control.Monad
import qualified Data.ByteString.Char8 as C
import Data.List
import Data.Ord
import qualified Data.Vector.Unboxed as U
import qualified Data.Vector.Unboxed.Mutable as UM

r :: Int -> IO (U.Vector Int)
r n = U.unfoldrN n (C.readInt . C.dropWhile (==' ')) <$> C.getLine

r' :: IO [Int]
r'  =   unfoldr    (C.readInt . C.dropWhile (==' ')) <$> C.getLine

lim = 1000010
main = do
    n <- readLn :: IO Int
    as <- sort<$>r'

    arr <- UM.replicate lim True

    solve arr (-1) as

    arrF <- U.freeze arr

    print =<< count arr as 0


solve :: UM.IOVector Bool -> Int -> [Int] -> IO ()
solve arr lst [] = return ()
solve arr lst (a:as)
    | lst == a  = do
        UM.write arr a False
        solve arr lst (dropWhile (==a) as) 
solve arr lst (a:as) = do
    b <- UM.read arr a
    when b $
        forM_ [a*2,a*3..lim-1] (\i -> UM.write arr i False)
    solve arr a as

count :: UM.IOVector Bool -> [Int] -> Int -> IO Int
count arr [] ac = return ac
count arr (a:as) !ac = do
    b <- UM.read arr a
    if b then count arr as (ac+1)
            else count arr as ac