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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

namespace CSharpSample01
{
    

    class Program
    {

        static int[] data;
        

        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());

            data = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();

            int cnt4 = 0;
            int cnt2 = 0;
            int cnt_uneven = 0;

            for(int i = 0; i < N; i++)
            {
                if(data[i] % 2 == 0)
                {
                    if(data[i] % 4 == 0)
                    {
                        cnt4++;
                    }
                    else
                    {
                        cnt2++;
                    }
                }
                else
                {
                    cnt_uneven++;
                }
            }            

            if (cnt_uneven <= cnt4)
            {
                Console.WriteLine("Yes");
                return;
            }
            else if (cnt_uneven == cnt4 + 1)
            {
                if (cnt2 > 0)
                {
                    Console.WriteLine("No");                  
                }
                else
                {
                    Console.WriteLine("Yes");                    
                }
                return;
            }

            Console.WriteLine("No");
            return;

        }
    }
}