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 static System.Math;

class AtCoder{
  public static void Main(){

    int n = int.Parse(Console.ReadLine());
    var input = Console.ReadLine().Split();
    int[] a = new int[n];
    int x4 = 0;
    int x2 = 0;
    for (int i = 0; i < n; i++)
    {
        a[i] = int.Parse(input[i]);
        if(a[i] % 4 == 0) x4++;
        else if(a[i] % 2 == 0) x2++;
    }

    bool b = false;
    if(x2 > 0 && 2 * x4 + x2 >= n) b = true;
    if(x2 == 0 && 2 * x4 + 1 >= n) b = true;

    if(b) Console.WriteLine("Yes");
    else Console.WriteLine("No");

  }
}