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: Wrong Answer)

#include<iostream>
#include<cstring>
using namespace std;
int INF=-100;
int n;
int b[100001],a[100001];
int dfs(int k)
{
    if(k==n)
    {
        return 1;
    }
    for(int i=1;i<n;i++)
    {
        if(a[i]!=INF)
        if((a[i]*b[k-1])%4==0)
        {
            b[k]=a[i];
            int sign=a[i];
            a[i]=INF;
            if(dfs(k+1))
            {
                return 1;
            }
            a[i]=sign;
        }
    }
    return 0;
}
int main()
{

   cin>>n;
   for(int i=0;i<n;i++)
    cin>>a[i];
    b[0]=a[0];
    if(dfs(1))
        cout<<"Yes"<<endl;
    else
        cout<<"No"<<endl;
    return 0;
}