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 Data.List.Split
import Data.Maybe
import qualified Data.ByteString.Char8 as B
main=mapM_(putStrLn.solve).chunksOf 2.map(map(fst.fromJust.B.readInt).B.words).B.lines=<<B.getContents
solve[[n],as]=if(c+(if b==1||b>1&&c/=0 then 1 else 0)<=(if a/=0 then a+1 else 0))then"Yes"else"No"
  where(a,b,c)=foldr f(0,0,0)as
f v(a,b,c)
  |v`mod`4==0=(a+1,b,c)
  |v`mod`2==0=(a,b+1,c)
  |otherwise=(a,b,c+1)