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 (3.8.2) (judge verdict: Accepted)

n = int(input())
a = list(map(int,input().split()))
b1 = 0
b2 = 0
b4 = 0
for i in range(n):
    c = 0
    while a[i] % 2 == 0:
        c += 1
        a[i] /= 2
    if c == 0:
        b1 += 1
    elif c == 1:
        b2 += 1
    else:
        b4 += 1
if b2 == 0:
    if b1 <= b4 + 1:
        print('Yes')
    else:
        print('No')
else:
    if b1 <= b4:
        print('Yes')
    else:
        print('No')