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()
{
	int n,a1=0,a2=0,a4=0;
	cin>>n;
	for(int i=0;i<n;i++){
		int t;
		cin>>t;
		if(t%4==0)
			a4++;
		else if(t%2==0)
			a2++;
		else a1++;
	}
	if(a1<=a4&&a2>0)
		cout<<"Yes"<<endl;
	else if(a2==0&&a1<=a4+1)
	cout<<"Yes"<<endl;
		else cout<<"No"<<endl;
	return 0;
}