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)

using namespace std;

#include <iostream>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <limits>
#include <climits>
#include <vector>
#include <string>
#include <set>
#include <queue>
#include <stack>
#include <map>
#include <numeric>
typedef long long ll;
typedef pair<int,int> p;

int main()
{
  int n;
  cin >> n;
  vector<ll> v(n,0);
  int countA = 0;
  int countB = 0;
  int countC = 0;
  for (int i = 0; i < n; i++)
  {
    cin >> v[i];
    if (v[i] % 4 == 0){
      countA++;
    }else if (v[i] % 2 == 0){
      countB++;
    }else{
      countC++;
    }
  }

  countB %= 3;

  if (countB % 2 == 0)
  {
    if ((countC <= countA * 2))
    {
      cout << "Yes" << endl;
    }else{
      cout << "No" << endl;
    }
  }else{
    if (countA * 2 >= countB + countC)
    {
      cout << "Yes" << endl;
    }else{
      cout << "No" << endl;
    }
  }
}