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: Wrong Answer)

using System;
using System.Text;
using System.Collections.Generic;
using System.Linq;
class Solve
{
    public static void Swap<T>(ref T a, ref T b)
    {
        T tmp = a;
        a = b;
        b = tmp;
    }

    public static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        int[] a = Console.ReadLine().Split().Select(int.Parse).OrderBy(e=>e).ToArray();
        
        for (int i = 0; i < (n - 1); i++)
        {
            bool flag = false, koukan = false;
            int b = a[i], c = a[i + 1];
            int d = 0;
            int e = 0;
            for (int j = i + 2; j < n; j++)
            {
                d = ((b % 4) * (c % 4)) % 4;
                if (j >= n) break;
                Console.WriteLine($"n:{n},i:{i},j:{j}");
                if (d != 0)
                {
                    c = a[j];
                    koukan = true;
                    e = j;
                }
                else
                {
                    flag = true;
                    break;
                }

            }
            d = ((b % 4) * (c % 4)) % 4;
            if (d == 0)
            {
                flag = true;
            }

            if (!flag)
            {
                Console.WriteLine("No");
                return;
            }
            if (koukan)
                Swap(ref a[i + 1], ref a[e]);
        }
        Console.WriteLine("Yes");
        return;

    }
}