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 Python (3.4.3) (judge verdict: Accepted)

N=int(input())
cnt={1:0,2:0,4:0}
for a in map(int,input().split()):
    if a%4==0:cnt[4]+=1
    elif a%2==0:cnt[2]+=1
    else:cnt[1]+=1

if cnt[1]>0:
    cnt[1]-=1
    bef=1
elif cnt[2]>0:
    cnt[2]-=1
    bef=2
else:
    cnt[4]-=1
    bef=4

flag=True
for i in range(N-1):
    if bef==1:
        if cnt[4]==0:
            flag=False
            break
        cnt[4]-=1
        bef=4
    elif bef==4:
        if cnt[1]>0:
            cnt[1]-=1
            bef=1
        elif cnt[2]>0:
            cnt[2]-=1
            bef=2
        else:
            cnt[4]-=1
            bef=4
    elif bef==2:
        if cnt[2]>0:
            cnt[2]-=1
            bef=2
        else:
            if cnt[4]==0:
                flag=False
                break
            cnt[4]-=1
            bef=4
if flag:print('Yes')
else:print('No')