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;
  cin >>N;
  vector<int> a(N);
  int zeros=0,ones=0,twoes=0;
  for(int i=0;i<N;i++){
    cin >>a[i];
    if(a[i]%2 != 0){
      a[i]=0;
      zeros++;
    }
    else if(a[i]%4 != 0){
      a[i]=1;
      ones++;
    }
    else{
      a[i]=2;
      twoes++;
  }
  if(twoes>=zeros) cout << "Yes" <<endl;
  else cout << "No" <<endl;
}