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)

#include <algorithm>
#include <cmath>
#include <cstdlib>
#include <iostream>
#include <map>
#include <vector>
using namespace std;
typedef long long int ll;

int main(int argc, char const *argv[]) {
  ll N;
  cin >> N;
  vector<ll> a(N);
  vector<bool> able_divided_by_only_two(N, false);
  ll num_of_two = 0;
  ll num_of_four = 0;
  vector<bool> able_divided_by_four(N, false);
  for (size_t i = 0; i < a.size(); i++) {
    cin >> a[i];
    if (a[i] % 4 == 0) {
      // able_divided_by_four[i] = true;
      num_of_four++;
    } else if (a[i] % 2 == 0) {
      // able_divided_by_only_two[i] = true;
      num_of_two++;
    }
  }
  // cout << "four;" << num_of_four << " two;" << num_of_two << endl;
if(num_of_two==0){
  if(N-num_of_four>num_of_four+1){
    cout<<"No"<<endl;
    return 0;
  }else{
    cout<<"Yes"<<endl;
    return 0;
  }
}


  if (N - num_of_four - num_of_two > num_of_four ) {
    cout << "No" << endl;
    return 0;
  } else {
    cout << "Yes" << endl;
    return 0;
  }

  return 0;
}