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() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  long n;
  cin >> n;
  long long a;
  long long m = 0;
  long long k = 0;
  bool is4 = false;
  bool isNo = false;
  long i;
  for (i = 0; i < n; i++) {
    cin >> a;
    if (a % 4 == 0) m++;
    if (a == 2) k++;
  }
  for (i = 0; i < n;) {
    if (!is4 && 0 < k) {
      i += k;
      k = 0;
      is4 = true;
    } else if (is4 && 0 < m) {
      m--;
      is4 = false;
      i++;
    } else if (!is4) {
      i++;
      is4 = true;
    } else {
      isNo = true;
      break;
    }
  }
  if (isNo)
    cout << "No" << endl;
  else
    cout << "Yes" << endl;
  return 0;
}
