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)

def multiples_of(num)
  if num % 4 == 0
    4
  elsif num % 4 != 0 && num % 2 == 0
    2
  else
    1
  end
end

n = gets.to_i
nums = gets.split.map(&:to_i)
memo = Hash.new(0)
nums.each do |num|
  memo[multiples_of(num)] += 1
end
ans = [4]
n.times do |i|
  case ans[i]
  when 1
    if memo[4] > 0
      memo[4] -= 1
      ans << 4
    else
      puts "No"
      exit
    end
  when 2
    if memo[2] > 0
      memo[2] -= 1
      ans << 2
    elsif memo[4] > 0
      memo[4] -= 1
      ans << 4
    else
      puts "No"
      exit
    end
  when 4
    if memo[1] > 0
      memo[1] -= 1
      ans << 1
    elsif memo[2] > 0
      memo[2] -= 1
      ans << 2
    elsif memo[4] > 0
      memo[4] -= 1
      ans << 4
    else
      puts "No"
      exit
    end
  end
end
puts "Yes"