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: Accepted)

{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE OverloadedStrings #-} 
import qualified Data.Text.Lazy as T
import qualified Data.Text.Lazy.IO as TIO
import Data.Monoid
import Data.List
import qualified Data.Vector.Unboxed as V

main = do
  input <- TIO.getContents
  let ls = T.lines input 
      n = ls !! 0
      l :: V.Vector Int
      l =   V.fromList $ fmap ( read .T.unpack) $ T.words $ ls !! 1      
      (!s0,!s2,!s4) = V.foldl f (0,0,0) l
        where f  (s0,s2,s4) a  | (a `mod` 4) == 0 = (s0, s2, s4 + 1)
                               | (a `mod` 2 ) == 0 =  (s0, s2 + 1, s4)
                               | otherwise =  (s0 + 1, s2 , s4)
      getR (s0,s2,s4) | (s0<=s4) || ( s0 == s4+1 && s2 == 0 ) = "Yes"  
                      | otherwise = "No"
  Prelude.putStr $  getR (s0,s2,s4)