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: Time Limit Exceeded)

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
int n,a[100005],flag=0;
int main(int argc, char *argv[])
{
	int s1=0,s2=0;
	cin>>n;
	for(int i=0;i<n;i++)
	{
		cin>>a[i];
		if(a[i]%2)s1++;
		else s2++;
	}
	sort(a,a+n);
	//cout <<"s1 == "<<s1<<" ,s2 == "<<s2<<".\n";
	if(s1>s2+1)cout <<"No"<<endl;
	else
	{
		do
		{
			int i;
			/*for(i=0;i<n;i++)
			cout <<a[i]<<" ";
			cout <<endl;*/
			for(i=1;i<n;i++)
			{
				if(a[i]*a[i-1]%4!=0)break;
			}
			if(i==n)flag=1;
			if(flag)
			{
				//for(i=0;i<n;i++)cout<<a[i]<<" ";
				//cout<<endl;
				break;
			}
		}while(next_permutation(a,a+n));
		
		if(flag)cout <<"Yes"<<endl;
		else cout <<"No"<<endl;
	}
}