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>
const long long maxn = 1e5 + 10;
int fn, tn, n, odd;
int main() {
  while (~scanf("%d", &n)) {
    fn = tn = odd = 0;
    for (int i = 1; i <= n; i++) {
      long long x;
      scanf("%lld", &x);
      if (x & 1) odd++;
      if (x % 4 == 0)
        fn++;
      else if (x % 2 == 0)
        tn++;
    }
    if (2 * fn + 1 >= (n - 1 - tn / 2) || tn == n || fn + tn >= n ||
        fn >= 1 && odd == 1 || fn >= 2 && odd == 2)
      printf("Yes\n");
    else
      printf("No\n");
  }
  return 0;
}
