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 collections
n,ais = int(raw_input()), map(int, raw_input().split())
cc = collections.Counter()
for ai in ais:
	if ai % 4 == 0: cc[0] += 1
	elif ai % 2 == 0: cc[1] += 1
	else: cc[2] += 1

q,h = collections.deque([0]), [[2,1,0],[1],[0]] 
while(n):
	b = False
	for u in h[q[-1]] + [-1]:
		if u == -1: b = True
		if cc[u] > 0:
			q.append(u)
			
			cc[u] -=1
			n -=1
			break
	if b: break

print 'Yes' if n == 0 else 'No'