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)

N = gets.to_i
line = gets
data = line.split(" ")
odd = Array.new
even = Array.new
multiples_four = Array.new
N.times do |i|
  num = data[i].to_i
  if num % 4 == 0
    multiples_four << num
  elsif num % 2 == 0
    even << num
  else
    odd << num
  end
end
if even.length == 0
  if odd.length <= multiples_four.length + 1
    puts "Yes"
  else
    puts "No"
  end
elsif odd.length > 0
  if odd.length <= multiples_four.length
    puts "Yes"
  else
    puts "No"
  end
else
  if multiples_four == 0
    puts "No"
  else
    puts "Yes"
  end
end