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)

-- https://github.com/minoki/my-atcoder-solutions
{-# LANGUAGE TypeApplications #-}
-- {-# LANGUAGE BangPatterns #-}
import Data.Char (isSpace)
import Data.List (unfoldr)
import Control.Monad
import qualified Data.Vector.Unboxed as U
import qualified Data.Vector.Unboxed.Mutable as UM
import qualified Data.ByteString.Char8 as BS

main = do
  n <- readLn @Int
  xs <- U.unfoldrN n (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
  let m = U.maximum xs
  let vec :: U.Vector Int
      vec = U.create $ do
        vec <- UM.replicate (m+1) 0
        U.forM_ xs $ \x -> do
          UM.modify vec (+ 1) x
          forM_ [2*x,3*x..m] $ \i -> do
            UM.modify vec (+ 2) i
        return vec
  print $ length [ () | x <- U.toList xs, vec U.! x <= 1 ]