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`.

Examples

Input

3
1 10 100


Output

Yes


Input

4
1 2 3 4


Output

No


Input

3
1 4 1


Output

Yes


Input

2
1 1


Output

No


Input

6
2 7 1 8 2 8


Output

Yes
import numpy as np
N = int(input())
a = np.array([int(i) for i in input().split()] )

log2_a = np.log2(a).astype(int)*(a%2==0)
c2 = np.sum(log2_a == 1)
c4 = np.sum(log2_a > 1)
c1 = N - c2 - c4

if c2:
    print("Yes" if c4 >= c1 else "No")
elif c4 and c4 + 1 >= c1:
    print("Yes")
else:
    print("No")

