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 (Clang 3.8.0) (judge verdict: Accepted)

//
// Created by Akifumi Ohata on 2017/10/03.
//


#include<iostream>
#include <vector>
#include <numeric>
#include <math.h>
#include <cmath>
#include <algorithm>
#include <iomanip>

using namespace std;

using ll =  long long int;

int main() {
    ios::sync_with_stdio(false);

    int N;
    cin >> N;


    std::vector<int> Arrays;
    for(int i=0;i<N ;i++){

        int tmp=0;
        cin >> tmp;
        int time=0;

        if(tmp%2==0){

            time=1;
        }


        if(tmp%4==0){

            time=2;
        }

        Arrays.push_back(time);

    }


    int num_zero= static_cast<int>(std::count(Arrays.begin(), Arrays.end(), 0));
    int num_one= static_cast<int>(std::count(Arrays.begin(), Arrays.end(), 1));
    int num_tow= static_cast<int>(std::count(Arrays.begin(), Arrays.end(), 2));


    if(num_zero <= num_tow){

        cout << "Yes" << endl;

    }


    if(num_zero > num_tow){

        if (num_zero-num_tow >= 2){
            cout << "No" << endl;
        }

        if (num_zero-num_tow == 1){

            if(num_one==0){
            cout << "Yes" << endl;
            }else{
                cout << "No" << endl;

            }
        }

    }



    return 0;
}