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
A = gets.split.map(&:to_i)

n = N
f = A.count{ |a| a % 4 == 0 }
e = A.count{ |a| a % 2 == 0 }
o = N - e
t = e - f

ans = "Yes"

b = Array.new(N+1)
b[0] = 4

1.upto N do |i|
  
  if b[i-1] % 4 == 0
    if o > 0
      o -= 1
      b[i] = 1
    elsif t > 0
      t -= 1
      b[i] = 2
    else
      f -= 1
      b[i] = 4
    end
  elsif b[i-1] % 4 == 2
    if t > 0
      t -= 1
      b[i] = 2
      elsif f > 0
      f -= 1
      b[i] = 4
    else
      ans = "No"
      break
    end
  else
    if f > 0
      f -= 1
      b[i] = 4
    else
      ans = "No"
      break
    end
  end
end
    
puts ans