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.Linq;
using System.Collections.Generic;
using System.Numerics;
using static System.Console;

class Program {
    internal static void Main(string[] args) {
        var N = int.Parse(ReadLine());
        var a = ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();

        var cnt = a.Count(i => i % 4 == 0);

        var hoge = 2;
        if (N <= 3) { hoge = 1; }
        if (cnt < hoge) {
            WriteLine("No");
            return;
        }

        if (N >= 6) {
            var even = a.Count(i => i % 2 == 0);
            if (N - 4 > even && (N - 4) / 2 > cnt) {
                WriteLine("No");
                return;
            }
        }

        WriteLine("Yes");
    }
}