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() {
  long long n;
  scanf("%lld", &n);
  long long inp[n];
  for (int i = 0; i < n; i++) scanf("%lld", &inp[i]);
  long long cnt[3] = {0};
  for (int i = 0; i < n; i++) {
    if (inp[i] % 4 == 0)
      cnt[2]++;
    else if (inp[i] % 2 == 0)
      cnt[1]++;
  }
  int group = n / 3;
  long long rem = n % 3;
  bool ok = false;
  cnt[2] -= group;
  if (cnt[2] >= 0) {
    if (rem > 0 && cnt[2] > 0) ok = true;
    if (rem == 1 && cnt[1] > 2) ok = true;
    if (rem > 0 && cnt[1] > n) ok = true;
    if (rem == 0) ok = true;
  } else {
    rem = -cnt[2] * 3 + rem;
    if (rem == 1 && cnt[1] > 2) ok = true;
    if (rem > 1 && cnt[1] >= rem) ok = true;
  }
  printf("%s\n", ok ? "Yes" : "No");
  return 0;
}
