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 mark[100001];
int count = 0;
int a[100001];
bool flag = false;
void DFS(int tmp) {
  if (count == N) {
    flag = true;
    return;
  }
  for (int i = 0; i < N; i++) {
    if (mark[i] == 1 && ((tmp % 4) * (a[i] % 4)) % 4 == 0) {
      mark[i] = 0;
      count++;
      DFS(a[i]);
      mark[i] = 1;
      count--;
    }
    if (flag) return;
  }
}
int main() {
  scanf("%d", &N);
  for (int i = 0; i < N; i++) {
    scanf("%d", &a[i]);
    mark[i] = 1;
  }
  for (int i = 0; i < N; i++) {
    if (a[i] % 4 == 0) continue;
    mark[i] = 0;
    count++;
    DFS(a[i]);
    mark[i] = 1;
    count--;
    if (flag) break;
  }
  if (flag)
    printf("Yes\n");
  else
    printf("No\n");
  return 0;
}
