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 Lua (Lua 5.3.5) (judge verdict: Wrong Answer)

local read = io.read

local n = read("n")

local n_minus = n
local two_times_count = 0
for i = 1, n do
	local a_i = read("n")
	if a_i % 4 == 0 then
		n_minus = n_minus - 3
	elseif a_i % 2 == 0 then
		two_times_count = two_times_count + 1
	end
end

if two_times_count == 0 then
elseif two_times_count % 2 == 0 then
	n_minus = n_minus + 1 - two_times_count // 2 * 2
elseif two_times_count % 2 == 1 then
	n_minus = n_minus - two_times_count // 2 * 2
end

print((n_minus <= 0) and "Yes" or "No")