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)

-- 4-adjacent.hs --- 4-adjacent

-- author: Seong Yong-ju <sei40kr@gmail.com>

inspect :: [Int] -> (Int, Int)
inspect [] = (0, 0)
inspect (a:as) =
  (c1 + (if a `mod` 2 /= 0 then 1 else 0), c2 + (if a `mod` 4 == 0 then 1 else 0))
  where
    (c1, c2) = inspect as

solve :: [Int] -> Bool
solve as = c1 <= c2
  where
    (c1, c2) = inspect as

main :: IO ()
main = do
  n <- (read :: String -> Int) <$> getLine
  as <- take n . map (read :: String -> Int) . words <$> getLine
  putStrLn $ if solve as then "Yes" else "No"