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;
  int twos, fours, nons;
  twos = fours = nons = 0;
  const int MAXN = 1e5 + 5;
  vector<int> a(MAXN, 0);
  cin >> N;
  for (int i = 1; i <= N; ++i) {
    cin >> a[i];
    if ((a[i] % 2) != 0) {
      ++nons;
    } else {
      if ((a[i] % 4) == 0) {
        ++fours;
      } else {
        ++twos;
      }
    }
  }
  bool failure = false;
  for (int i = 1; i <= N - 1; ++i) {
    if ((a[i] % 2) != 0) {
      if (fours) {
        --fours;
      } else {
        failure = true;
      }
    } else {
      if ((a[i] % 4) == 0) {
        if (nons)
          --nons;
        else if (twos)
          --twos;
        else
          --fours;
      } else {
        if (twos)
          --twos;
        else if (fours)
          --fours;
        else
          failure = true;
      }
    }
  }
  if (failure or (fours < 0) or (twos < 0) or (nons < 0))
    cout << "No" << endl;
  else
    cout << "Yes" << endl;
  return 0;
}
