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 <bits/stdc++.h>

using namespace std;

int main() {

	int n, x, qtd4=0, qtd2=0;

	scanf("%d", &n);

	for (int i=0; i<n; ++i) {
		scanf("%d", &x);

		if (x%4 == 0) {
			++qtd4;
		}
		else if (x%2 == 0) {
			++qtd2;
		}
	}

	if (qtd4 >= n/2)
		puts("Yes");
	else if (qtd4 >= ceil((n-qtd2+1)/2))
		puts("Yes");
	else 
		puts("No");

	return 0;
}