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: Wrong Answer)

{-# LANGUAGE PartialTypeSignatures #-}
{-# LANGUAGE BangPatterns #-}
module Main (main) where

import qualified Data.ByteString.Char8 as C8
import qualified Data.Char as C
import qualified Data.List as L

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

g :: [Int] -> [Int]
g [] = []
g (x:xs) = x : g (filter (\y -> x `mod`y == 0) xs)

solve :: Int -> [Int] -> _
solve n xs = go 0 1 1 xs xs
  where
    go !c !i !j [] _ = c
    go !c !i !j (y:ys) [] = go (c+1) (i+1) 1 ys xs
    go !c !i !j a@(y:ys) (z:zs) =
      if i == j
        then go c i (j+1) a zs
        else if y `mod` z == 0
              then go c (i+1) 1 ys xs
              else go c i (j+1) a zs

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

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