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: Accepted)

N = int(input())

A = list(map(int, input().split()))

nl = [0] * 3

for a in A:
  if a % 4 == 0:
    nl[2] += 1
  elif a % 2 == 0:
    nl[1] += 1
  else:
    nl[0] += 1

# 2は2個以上あればとりあえず全部繋げとけば良い、1個だけなら１としてカウント同じ
if nl[1] == 1:
  nl[0] += 1

# 2が2個以上あれば、2.....2,4,1,4,1 num_4 >= num_1の形を満たせばOK
# ２が1,0個なら、1,4,1,4,...4,1 num_4 + 1 >= num_1の形を満たせばOK
if nl[1] >= 2 and nl[2] >= nl[0]:
  print("Yes")
elif nl[1] <= 1 and nl[2] >= nl[0] - 1:
  print("Yes")
else:
  print("No")