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(void)
{
	int a1=0, a2=0, a4=0;
	int i, n,x；
	cin >> n;
	for (i = 0; i < n; i++) 
	{
		cin >> x;
		if (x % 4 == 0)
			a4++;
		else if (x % 2 == 0)
			a2++;
		else
			a1++;
	}
	if ((a2 == 0)&& (a4 >= (a1 - 1)))
	{
		cout << "YES";
	}
	else if ((a4 >= a1)&&(a2>0))
	{
		cout << "YES";
	}
	else
		cout << "NO";
	return EXIT_SUCCESS;
}