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>
using namespace std;

int main()
{
    int n;
    int num;
    cin >> n;
    int odd_counter = 0;
    int even_counter = 0;
    int forth_counter = 0;
    for(int i = 0; i < n; ++i)
    {
        cin >> num;
        if(num % 4 == 0) forth_counter++;
        else if(num % 2 == 0) odd_counter++;
        else even_counter++;
    }
    if(forth_counter ==  even_counter)
    {
        if(odd_counter % 2 == 0)
        {
            cout << "YES" << endl;
        }
        else if(odd_counter % 2 != 0 && odd_counter == 1)
        {
            cout << "YES" << endl;
        }
        else
        {
            cout << "NO" << endl;
        }
    }
    else
    {
        if(odd_counter != 0 || forth_counter != 0)
        {
            if(odd_counter % 2 == 0 || forth_counter % 2 == 0)
            {
                cout << "YES" << endl;
            }
            else
            {
                cout << "NO" << endl;
            }       
        }
        else
        {
            cout << "NO" << endl;
        }
    }

    return 0;
}