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: Accepted)

#include <bits/stdc++.h>
#define REP(i, n) for(int i = 0; i < n; i++)
#define REPR(i, n) for(int i = n; i >= 0; i--)
#define FOR(i, m, n) for(int i = m; i < n; i++)
#define INF 2e9
#define MOD 1000000007
#define ALL(v) v.begin(), v.end()
using namespace std;
typedef long long ll;
using P = pair<int,int>;
  
int main()
{
  int N;
  cin >> N;
  int odd=0;
  int four=0;
  vector<int> A(N);
  REP(i, N){
    cin >> A[i];
    if(A[i]%2==1){
      odd++;
    }else if(A[i]%4==0){
      four++;
    }
  }

  if(odd-1<=four){
    if(odd<=four){
      cout << "Yes" << endl;
    }else{
      if(odd+four==N){
        cout << "Yes" << endl;
      }else{
        cout << "No" << endl;
      }
    }
  }else{
    cout << "No" << endl;
  }
  
  
}