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;
using System.Text;

namespace AtCoder
{
	class Program
	{
		static void Main(string[] args)
		{
			Question.Exec();
		}
	}

	public static class Question
	{
		public static bool IsOdd(long n)
		{
			bool isOdd = n % 2 == 1;
			return isOdd;
		}

		public static void Exec()
		{
			var n = long.Parse(Console.ReadLine());
			var array = Console.ReadLine().Split(' ').Select(i => long.Parse(i)).ToArray();
			var list = array.ToList();

			var oddList = list.Where(x => IsOdd(x)).ToList();
			var noOddList = list.Where(x => IsOdd(x) == false).ToList();

			bool isOK = false;
			if (oddList.Count == 0)
			{
				isOK = true;
			} else if (oddList.Count - 1 <= noOddList.Count)
			{
				var list4 = noOddList.Where(x => x % 4 == 0).ToList();
				if (noOddList.Count - list4.Count == 0 && oddList.Count <= list4.Count + 1)
				{
					isOK = true;
				} else if (oddList.Count <= list4.Count)
				{
					isOK = true;
				}
			}

			if (isOK) {
				Console.WriteLine($"Yes");
			} else {
				Console.WriteLine($"No");
			}

			Console.ReadKey();
		}
	}
}