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`.

Examples

Input

3
1 10 100


Output

Yes


Input

4
1 2 3 4


Output

No


Input

3
1 4 1


Output

Yes


Input

2
1 1


Output

No


Input

6
2 7 1 8 2 8


Output

Yes
#include <bits/stdc++.h>
using namespace std;
int main() {
  int N, ans;
  bool yatta = false;
  cin >> N;
  vector<int> a(N), an(N);
  vector<bool> tta(N, false);
  for (int i = 0; i < N; i++) {
    cin >> a.at(i);
  }
  tta.at(0) = true;
  sort(a.begin(), a.end());
  an.at(0) = a.at(0);
  for (int i = 1; i < N; i++) {
    for (int j = 1; j < N; j++) {
      if (tta.at(j) == true) {
        continue;
      } else if ((an.at(i - 1) * a.at(j)) % 4 == 0) {
        an.at(i) = a.at(j);
        tta.at(j) = true;
        break;
      }
    }
  }
  ans = *min_element(an.begin(), an.end());
  if (ans == 0) {
    cout << "No" << endl;
    yatta = true;
  }
  if (yatta == false) {
    cout << "Yes" << endl;
  }
}
