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<iostream>
#include<vector>
#include<algorithm>
#include<map>
#include<cstring>
#include<math.h>
#include<bitset>
#include<queue>
#include<set>
#include<iomanip>
#include<math.h>
// #include<bits/stdc++.h>
using namespace std;
#define ll long long
constexpr long long int INFLL = 1001001001001001LL;
constexpr int INFI = 1000000007;

int main(){
  int N;
  cin >> N;
  vector<ll> a(N);
  int N_0=0,N_2=0,N_4=0;
  for(int i=0; i<N; i++){
    cin >> a[i];
    if(a[i]%4 == 0){
      N_4++;
    }else if(a[i]%2 == 0){
      N_2++;
    }else{
      N_0++;
    }
  }
  if(N_0 == 0){
    cout << "Yes" << endl;
    return 0;
  }
  if(N_2 == 0){
    if(N_0 <= N_4+1){
      cout << "Yes" << endl;
      return 0;
    }
  }else{
    if(N_0 <= N_4){
      cout << "Yes" << endl;
      return 0;
    }
  }
  cout << "No" << endl;
  return 0;
}