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 Ruby (2.3.3) (judge verdict: Accepted)

# 奇数が絡んできた場合だけできない可能性がある
# 奇数の数をk、4の倍数であって2の倍数でない数をfとすると k f k f や f k fはok 
# 2の倍数であって4の倍数でないやつはどっか適当に影響しないとこ（両端とか）においとけばいいので考えないで済む
# ↑間違い 1WA
# 2の倍数であって4の倍数でないやつをbとすると
# k f k f k (S(f)-1>=S(k))は大丈夫だが
# b b k f k f k b b b とかはダメ
# 
# S(f)>=S(k)

n = gets.chomp.to_i
odd_n, two_n, four_n = 0, 0, 0
gets.chomp.split.map(&:to_i).each do |ai|
  if ai.odd?
    odd_n+=1
  elsif ai%4==0
    four_n+=1
  else
    two_n+=1
  end
end
if four_n>=odd_n-1 && two_n == 0
  puts "Yes"
elsif four_n>=odd_n
  puts "Yes"
else
  puts "No"
end