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`.

Examples

Input

3
1 10 100


Output

Yes


Input

4
1 2 3 4


Output

No


Input

3
1 4 1


Output

Yes


Input

2
1 1


Output

No


Input

6
2 7 1 8 2 8


Output

Yes
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();
	}
}
