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)

import qualified Data.Vector.Unboxed as V
import qualified Data.ByteString.Char8 as B
import Data.Maybe (fromJust)

main :: IO ()
main = do
    _ <- B.getLine
    as <- V.fromList . map (fst . fromJust . B.readInt) . B.words <$> B.getLine
    let (v1, vs) = V.unstablePartition odd as
        v4 = V.filter (\x -> x `mod` 4 == 0) vs
    let b1 = V.length v1
        b4 = V.length v4
        b2 = V.length as - b1 - b4
    putStrLn $ if b2 == 0
                then if b1 <= b4 + 1 then "Yes" else "No"
                else if b1 <= b4     then "Yes" else "No"