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: Time Limit Exceeded)

import Data.List

factors :: Int -> Int -> Int
factors f a
    | a `mod` f /= 0 = 0
    | otherwise = 1 + factors f (a `div` f)

order :: [Int] -> [Int]
order [] = []
order (x:[]) = [x]
order xs = head xs : last xs : order (init $ tail xs)

solve :: [Int] -> String
solve xs =
    let fs = sort $ map (factors 2) xs
        ordered = order fs
        sums = zipWith (+) ordered (tail ordered)
    in if all (>=2) sums then "Yes\n" else "No\n"

main = interact $ (solve . map read . tail . words)