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 Control.Applicative
main = do
    n <- getLine
    a <- map read . words <$> getLine
    putStrLn $ solve a
solve :: [Int] -> String
solve list = if judge tuple then "Yes" else "No"
    where tuple = count list

powerTwo :: Int -> Int -> Int
powerTwo n x = if r==0 then powerTwo (n+1) q else n
    where (q,r) = divMod x 2

count :: [Int] -> (Int,Int,Int)
count = foldl f (0,0,0)
    where f (x,y,z) n = case powerTwo 0 n of 0 -> (x+1,y,z)
                                             1 -> (x,y+1,z)
                                             _ -> (x,y,z+1)
judge :: (Int,Int,Int) -> Bool
judge (x,y,z) = if y>=1
                then x<=z
                else x<=z+1