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>

int main() {
	int n;
	std::cin >> n;

	int count2 = 0, count4 = 0;
	for (int i = 0; i < n; ++i) {
		int a;
		std::cin >> a;
		
		if (a % 4 == 0)
			++count4;
		else if (a % 2 == 0)
			++count2;
	}

	if (count4 + count2 / 2 >= n / 2)
		std::cout << "Yes" << std::endl;
	else
		std::cout << "No" << std::endl;
}