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 argc, char const *argv[]) {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  int ara[100010];
  int cnt = 0;
  for (int i = 1; i <= n; i++) {
    cin >> ara[i];
    if (ara[i] % 4 == 0) ara[i] %= 4;
    if (ara[i] == 0) cnt++;
  }
  sort(ara + 1, ara + n + 1);
  bool found = true;
  int ind = 0;
  for (int i = 1; i <= n; i++) {
    if (ara[i] != 0) {
      found = false;
      ind = i;
      break;
    }
  }
  if (found) {
    cout << "Yes" << endl;
    return 0;
  }
  int k[100010] = {0};
  k[1] = ara[ind];
  int num = 0;
  for (int i = ind + 1; i <= n; i++) {
    ara[i] = (ara[i - 1] * ara[i]) % 4;
    if (ara[i] != 0) num++;
  }
  if (cnt >= num) {
    cout << "Yes" << endl;
  } else
    cout << "No" << endl;
  return 0;
}
