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;
using static System.Math;
using static System.Console;
using static CS_Contest.Utils;

namespace CS_Contest {
	using Li = List<int>;
	using LLi = List<List<int>>;
    class Program {
        static void Main(string[] args) {
			new Calc().Solve();
			return;
        }

		private class Calc {
			public void Solve() {
				int N = ReadInt();
				Li list = ReadInt(' ');
				int four = list.Count(x => x % 4 == 0);
				int two = list.Count(x => x == 2);
				int even = list.Count(x => x % 2 == 0) - four - two;

				if (list.All(x => x % 2 == 0)) {
					Yes();
					return;
				}

				if (four == 0&&N!=two) {
					No();
					return;
				}

				N -= two;

				if (N / 2 <= four) {
					if (two > 0 && (even == 0&(!(N%2==0||(N%2==1&&N/2+1<=four))))) {
						No();
						return;
					}
					Yes();
				}
				else No();
				return;
			}
		}
    }

	
	
    public static class Utils {
        public static void WL(this object obj) => WriteLine(obj);
        public static void WL(this string obj) => WriteLine(obj);
        public static void WL<T>(this IEnumerable<T> list) => list.ToList().ForEach(x => x.WL());
		public static int ReadInt() => int.Parse(ReadLine());
		public static List<int> ReadInt(char s) => ReadLine().Split(s).Select(int.Parse).ToList();
		public static long ReadLong() => long.Parse(ReadLine());
		public static List<long> ReadLong(char s) => ReadLine().Split(s).Select(long.Parse).ToList();
		public static void REP(int n,Action<int> act) {
			for (int i = 0; i < n; i++) {
				act(i);
			}
		}
		public static void Yes() => "Yes".WL();
		public static void No() => "No".WL();
    }
}