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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class Program
{
    public static void Main( )
    {
        int N = int.Parse( Console.ReadLine( ) );
        var A = Console.ReadLine( ).Split( ).Select( int.Parse ).ToArray( );
        int other = 0;
        int multipulsOf2 = 0;
        int multipulsOf4 = 0;

        for ( int i = 0; i < A.Length; i++ )
        {
            if ( A[ i ] % 4 == 0 ) multipulsOf4++;
            else if ( A[ i ] % 2 == 0 ) multipulsOf2++;
            else other++;
        }

        bool isOk;
        if ( multipulsOf2%2==0 )
        {
            isOk =  multipulsOf4 >= other - 1 ;

        }
        else
        {
            isOk = multipulsOf4 - other >= 0;
        }
        Console.WriteLine(isOk ? "Yes" : "No");

    }




}