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 <string>
using namespace std ;

string yorn(bool a){if(a) return "Yes" ; return "No" ;}

int main(){
	int n ; cin >> n ;
	int two = 0 ;
	int four = 0 ;
	for(int i=0;i<n;i++){
		int a ; cin >> a ;
		if(a%2==0) two++ ;
		if(a%4==0) four++ ;
	}
	two -= four ;
	cout << yorn(n/2<=four||2*four+two>=n) << endl ;
}
