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 n;
int a;
int main(void) {
  int i;
  int mltn2, mlt4;
  scanf("%d", &n);
  mltn2 = mlt4 = 0;
  while (n--) {
    scanf("%d", &a);
    if (a % 4 == 0)
      mlt4++;
    else if (a % 2 != 0)
      mltn2++;
  }
  if (mlt4 >= mltn2)
    printf("Yes\n");
  else
    printf("No\n");
  return 0;
}
