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<cmath>
#include<algorithm>
#include<bits/stdc++.h>
using namespace std;
#define ll long longz


int main(){
    int n;
    cin >>n;
    int a[n]={0};
    for(int i=0;i<n;i++){
        cin >>a[i];
    }
    int cnt1=0,cnt2=0;
    for(int i=0;i<n;i++){
        if(a[i]%4==0)
            a[i]=0,cnt1++;
        if(a[i]%2==0&&a[i]!=0)
            a[i]=0,cnt2++;
    }
    if(cnt2==0){
        if(cnt1>=n/2) cout<<"Yes"<<endl;
        else cout<<"No"<<endl;
    }
    else {
        if(cnt1+cnt2-1>=n/2)cout<<"Yes"<<endl;
        else cout<<"No"<<endl;
    }



}

