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;
	while(n--){
		int temp;
		cin>>temp;
		if(temp%4==0) a4++;
		else if(temp%2==0) a2++;
		else a1++;
	}
	if(a2==0){
		if(a4+1>=a1) cout<<"Yes";
		else cout<<"No";
	}else {
		if(a4>=a1) cout<<"Yes";
		else cout<<"No";
	}
	return 0;
}
