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;
  cin >> n;
  int cnt1 = 0, cnt2 = 0;
  for (int i = 0; i < n; i++) {
    int a;
    cin >> a;
    if (a % 4 == 0) {
      cnt1++;
    } else if (a == 2) {
      cnt2++;
    }
  }
  n -= (cnt1 * 3);
  if ((cnt2 > 1 && cnt2 >= n) || n <= 0) {
    cout << "Yes" << endl;
  } else {
    cout << "No" << endl;
  }
}
