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 n, a[100005], flag = 0;
int main(int argc, char *argv[]) {
  int s1 = 0, s2 = 0;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    if (a[i] % 2)
      s1++;
    else
      s2++;
  }
  sort(a, a + n);
  if (s1 > s2 + 1)
    cout << "No" << endl;
  else {
    do {
      int i;
      for (i = 1; i < n - 1; i++) {
        if (a[i] * a[i - 1] % 4 != 0) break;
      }
      if (i == n - 1) flag = 1;
      if (flag) break;
    } while (next_permutation(a, a + n));
    if (flag)
      cout << "Yes" << endl;
    else
      cout << "No" << endl;
  }
}
