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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#include<string>
#include<math.h>
using namespace std;
int main()
{
	int n,m;
	scanf("%d",&n);
	int flag4=0;
	int flag2=0;
	int flag=0;
	int flag0=0;
	for(int i=0;i<n;i++)
	{
        cin>>m;
        if(m%4==0)
		flag4++;
		else
		{
			if(m%2==0)
			{
				flag2++;
				flag=1;
			}
			else
			{
				flag0++;
			}
		}	
	}
	if(flag4>=flag2+flag0-1)
	cout<<"Yes"<<endl;
	else
	{
		if(flag&&flag4>=flag0)
		cout<<"Yes"<<endl;
		else
		cout<<"No"<<endl; 
	} 
}