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.Collections.Generic;
using System.Linq;
using System;
class Program
{
	static void Main()
	{
		var countStr = Console.ReadLine();
		int count = int.Parse(countStr);

		var line = Console.ReadLine();
		string[] array = line.Split(' ');

		uint fourM = 0;
		uint twoM = 0;
		uint notM = 0;

		for (int i = 0; i < count; i++)
		{
			int num = int.Parse(array[i]);
			if (num % 4 == 0)
			{
				fourM++;
			}
			else if (num % 2 == 0)
			{
				twoM++;
			}
			else
			{
				notM++;
			}
		}

		fourM += twoM / 2;
		notM += twoM % 2;

		if (fourM + 1 >= notM)
		{
			Console.WriteLine("Yes");
		}
		else
		{
			Console.WriteLine("No");
		}
	}
}