Problem:
Score : 400 points

Problem Statement

We have a sequence of length N, a = (a_1, a_2, ..., a_N).
Each a_i is a positive integer.

Snuke's objective is to permute the element in a so that the following condition is satisfied:

For each 1 ≤ i ≤ N - 1, the product of a_i and a_{i + 1} is a multiple of 4.

Determine whether Snuke can achieve his objective.

Constraints

2 ≤ N ≤ 10^5

a_i is an integer.

1 ≤ a_i ≤ 10^9

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

If Snuke can achieve his objective, print Yes; otherwise, print No.

Sample Input 1

3
1 10 100

Sample Output 1

Yes

One solution is (1, 100, 10).

Sample Input 2

4
1 2 3 4

Sample Output 2

No

It is impossible to permute a so that the condition is satisfied.

Sample Input 3

3
1 4 1

Sample Output 3

Yes

The condition is already satisfied initially.

Sample Input 4

2
1 1

Sample Output 4

No

Sample Input 5

6
2 7 1 8 2 8

Sample Output 5

Yes

Solution in Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Data.List
import Data.IORef
import Control.Monad

main = do
  n <- readLn :: IO Int
  cnt2 <- newIORef 0 :: IO (IORef Int)
  cnt4 <- newIORef 0 :: IO (IORef Int)

  let
    func :: Int -> IO()
    func x = do
      when (mod x 2 == 0 && mod x 4 /= 0) (modifyIORef cnt2 (+1))
      when (mod x 4 == 0) (modifyIORef cnt4 (+1))

  a <- getLine >>=  (mapM_ func) . (map read) . words

  readIORef cnt2 >>=
    \x -> readIORef cnt4 >>=
    \y -> putStrLn (yesno (((if x/=1 then x else 0)+(if y /= 0 then 2*y+(if x/=0 then 0 else 1) else 0)) >= n ))

  where
    yesno True = "Yes"
    yesno False = "No"