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;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder.Abc
{
    class QuestionD
    {
        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            //// 文字列の入力
            //string s = Console.ReadLine();

            //// 整数の入力
            //long n = long.Parse(Console.ReadLine());

            //// 文字列配列の入力
            //string[] inputStrArray = Console.ReadLine().Split(' ');

            //// 整数配列の入力
            //var inputLongArray = Console.ReadLine().Split(' ').Select(i => long.Parse(i)).ToArray();

            long n = long.Parse(Console.ReadLine());
            var datas = Console.ReadLine().Split(' ').Select(i => long.Parse(i)).ToArray();

            long count = 0;
            long count2 = 0;
            long length = datas.Count();

            foreach (var a in datas) {
                if (a % 4 == 0) {
                    count++;
                    continue;
                }

                if (a % 2 == 0) {
                    count2++;
                }
            }

            string result = "";
            var is2 = length % 2 == 0;
            var count22 = count2 % 2 == 0;

            if (length / 2 <= count) {
                result = "Yes";
            } else if (is2 && count22 && (length / 2 <= count - count2 + 1) && count2 >= 2) {

                result = "Yes";

            } else if (!is2 && count22 && (length / 2 <= count - count2) && count2 >= 2) {
                result = "Yes";

            } else {
                 result = "No";
            }

            Console.WriteLine(result);

            Console.Out.Flush();
        }
    }
}