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 <iostream>
using namespace std;
int main(void){
    int N; cin>>N;
    int k2=0,k4=0;
    int a;
    for(int i=0;i<N;i++){
        cin>>a;
        if(a%4==0){
            k4++;
        }else if(a%2==0){
            k2++;
        }
    }
    if(k4+k2/2>=N/2){
        cout<<"Yes"<<endl;
    }else{
        cout<<"No"<<endl;
    }
    
}
