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 <vector>
using namespace std;

int main()
{
    int n;
    cin >> n;

    vector<int> data(n);
    for (auto& i : data)
    {
        cin >> i;
    }

    int numOdd = 0;
    int numEven = 0;
    int numMultiple4 = 0;
    for (const auto& i : data)
    {
        if (i % 2 == 0)
            numEven++;
        else
            numOdd++;
        if (i % 4 == 0) numMultiple4++;
    }

    if (numMultiple4 >= (numOdd - data.size()%2))
    {
        cout << "YES" << endl;
    }
    else
    {
        cout << "NO" << endl;
    }
    
    return 0;
}