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)


#include <algorithm>
#include <iostream>
#include <vector>
#include <string>
#include <cmath>
#include <map>
#include <set>
#include <stack>
#include <queue>
using namespace std;



int main() {
  int N;
  cin >> N;

  long long a;
  int mod2 = 0, mod4 = 0;
  for (int i = 0; i < N; ++i) {
    cin >> a;
    if(a % 4 == 0) {
      mod4++;
      continue;
    }
    if(a % 2 == 0) {
      mod2++;
    }
  }

  //
  if(mod4 * 2 >= N){
    cout << "Yes" << endl;
    return 0;
  }

  if(mod4 * 2 + mod2 >= N){
    cout << "Yes" << endl;
    return 0;
  }

  cout << "No" << endl;
  return 0;
}