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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

n = int(input())
a_list = list(map(int, input().split()))
counts = [0] * 3
for a in a_list:
	if a%4 == 0:
		counts[0] += 1 		 
	elif a%2 == 0:
		counts[1] += 1
	else:
		counts[2] += 1
r = 'Yes' if counts[2] <= counts[0]+1 else 'No'
if r == 'Yes':
	two_v = counts[1]
	four_v = counts[0] - counts[2]
	mod = two_v%2	
	if mod == 0 or mod - four_v < 1:
		r = 'Yes'
	else:
		r = 'No'
print(r)