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;

class Program {
    static int ReadInt() { return int.Parse(Console.ReadLine()); }
    static int[] ReadInts() { return Console.ReadLine().Split().Select(int.Parse).ToArray(); }
    static string[] ReadStrings() { return Console.ReadLine().Split(); }

    static bool Calc(int[] xs) {
        int n2 = 0;
        int n4 = 0;
        int m = 0;
        foreach (var x in xs) {
            if (x % 4 == 0) n4++;
            else if (x % 2 == 0) n2++;
            else m++;
        }

        if (n2 > 0) {
            return n4 >= m;
        }
        else {
            return n4 + 1 >= m;
        }
    }

    static void Main() {
        ReadInt();
        var xs = ReadInts();
        var ok = Calc(xs);
        Console.WriteLine(ok ? "Yes" : "No");
    }
}