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>
int main(void) {
  int N, k, a[100000], amari, g, tmp, l;
  g = 1;
  scanf("%d", &N);
  for (k = 0; k <= N - 1; k++) {
    if (k < N - 1) {
      scanf("%d ", &a[k]);
    } else {
      scanf("%d", &a[k]);
    }
  }
  for (k = 0; k <= N - 2; k++) {
    amari = (a[k] * a[k + 1]) % 4;
    if (amari != 0) {
      if (a[k] % 2 == 0) {
        for (l = k + 1; a[l] % 2 != 0 || l <= N - 2; l++) {
        }
        tmp = a[k + 1];
        a[k + 1] = a[l];
        a[l] = tmp;
      } else {
        for (l = k; a[l] % 4 != 0 || l <= N - 2; l++) {
        }
        tmp = a[k + 1];
        a[k + 1] = a[l];
        a[l] = tmp;
      }
    }
  }
  for (k = 0; k <= N - 2; k++) {
    amari = (a[k] * a[k + 1]) % 4;
    if (amari != 0) {
      g = 0;
    }
  }
  if (g == 1) {
    printf("Yes\n");
  } else {
    printf("No\n");
  }
  return 0;
}
