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 atcoder01
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());

            string[] input = Console.ReadLine().Split();
            int[] T = new int[N];

            for (int i = 0; i < N; i++) T[i] = int.Parse(input[i]);

            //2を含む数
            int x2 = 0;
            int y4 = 0;
            for (int i = 0; i < N; i++)
            {
                if (T[i] == 2)
                {
                    x2++;
                    continue;
                }
                if ((T[i] % 2) == 0)
                {
                    y4++;
                }
            }
            if (x2 != 0) x2--;
            string out01 = "No";
            if ((y4 == 0) && (x2 == N-1))
            {
                out01 = "Yes";
            }
            else if ((y4 == 1) && (y4 * 3 + x2 >= N))
            {
                out01 = "Yes";
            }
            else if((y4 > 1) && (y4 * 2 + 1 + x2 >= N))
            {
                out01 = "Yes";
            }
            Console.WriteLine(out01);
        }
    }
}