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.Collections.Generic;
using System.Linq;

class Program
{
	static void Main()
	{
		var n = int.Parse(Console.ReadLine());
		var a = Array.ConvertAll(Console.ReadLine().Split(new[] { ' ' }), number => int.Parse(number));

		var fourCount = a.Count(num => num % 4 == 0);
		var twoCount = a.Count(num => num == 2);
		var oneCount = a.Count(num => num == 1);

		if (fourCount > 0) {
			var needs = a.Length / 2;
			if (twoCount >= 2) {
				if (a.Length % 2 == 0) {
					needs -= twoCount / 2;
				} else {
					needs -= (twoCount - 1) / 2;
				}
			}

			Console.WriteLine(fourCount >= needs ? "Yes" : "No");
		} else if (twoCount == a.Length) {
			//4の倍数がなくても、数値が全部2ならOK
			Console.WriteLine("Yes");
		} else {
			//ダメ
			Console.WriteLine("No");
		}


		//デバッグ実行での確認用。そのまま提出しても問題なし
		Console.ReadKey();
	}
}