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 N, gendo, nino = 0, saigo = 0, fg = 0;
  long long int num;
  cin >> N;
  vector<long long int> a;
  for (int i = 0; i < N; i++) {
    cin >> num;
    a.push_back(num);
  }
  gendo = N / 2;
  if (N % 2 != 0) {
    gendo++;
  }
  num = 0;
  for (int i = 0; i < N; i++) {
    if (a[i] % 4 != 0) {
      if (a[i] % 2 == 0) {
        nino++;
        if (nino >= 2) {
          num--;
        }
      }
      num++;
      if (gendo < num) {
        break;
      }
    } else {
      fg = 1;
    }
  }
  saigo = N - nino;
  if (saigo % 2 != 0 && nino >= 2) {
    if (gendo == num) {
      gendo = 0;
    }
  }
  if (gendo < num) {
    cout << "No" << endl;
  } else {
    if (fg == 0 && nino != N) {
      cout << "No" << endl;
    } else {
      cout << "Yes" << endl;
    }
  }
  return 0;
}
