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() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n, d8 = 0, n2 = 0, aux = 0;
  bool ans = false;
  cin >> n;
  vector<int> seq(n);
  for (int i = 0; i < n; i++) {
    cin >> seq[i];
    if (seq[i] % 4 == 0)
      d8++;
    else if (seq[i] == 2 or seq[i] % 4 == 2)
      n2++;
  }
  n2 /= 2;
  n -= n2;
  if (d8 >= n / 2)
    ans = true;
  else
    ans = false;
  if (ans)
    cout << "Yes\n";
  else
    cout << "No\n";
}
