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)

main::IO ()
main = do
    _ <- readLn::IO Int
    xs <- map read . words <$> getLine
    
    let two = length [x | x <- xs,x`mod`2 == 0,x`mod`4 /= 0] 
        four = length [x | x <- xs,x`mod`4 == 0] 
    putStrLn $ solve two four (length xs)

solve:: Int -> Int -> Int -> String
solve a b xs
    |a + b == 0 = "No" 
    |xs `div`2 <= b = "Yes"
    |xs - 2 <= a = "Yes"
    |2 <= b && xs - 4 <= a = "Yes"
    |otherwise = "No"