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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.PrintWriter;
import java.util.Scanner;

public class Main
{
	static Scanner in;
	static PrintWriter out;
	static void solve()
	{
		int N = in.nextInt();
		int[] a = new int[N];
		for(int i = 0; i < N; i++)
		{
			a[i] = in.nextInt();
		}
		int sum = 0;
		int sumi = 0;
		for(int i = 0; i < N; i++)
		{
			if(a[i] % 2 == 1)
			{
				sum += 1;
			}
			if(a[i] % 4 == 0)
			{
				sumi += 1;
			}
		}
		out.println(sum);
		out.println(sumi);
		if(N % 2 == 1)
		{
			if(sumi + 1 < sum)
			{
				out.print("No");
			}
			else
			{
				out.print("Yes");
			}
		}
		else
		{
			if(sumi < sum)
			{
				out.print("No");
			}
			else
			{
				out.print("Yes");
			}
		}
	}
	public static void main(String[] args)
	{
		in = new Scanner(System.in);
		out = new PrintWriter(System.out);
		solve();
		out.flush();
		out.close();
		in.close();
	}
}