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>
#include<vector>
#include<algorithm>
using namespace std;
using ll = long long;
int main(){
    ll n;
    cin >> n;
    ll x,f=0,k=0;
    for(ll i=0;i<n;i++){
        cin >> x;
        if(x%4==0)  f++;
        else if(x%2!=0) k++;
    }
    if(f>=k||(f==k-1&&f+k==n))    cout << "Yes";
    else    cout << "No";
    return 0;
}