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<cstdio>

int main()
{
	int n,a[100002];
	scanf("%d",&n);
	int num_2 = 0,num_4 = 0;
	int flag = 0;
	for(int i = 0;i < n;i ++)
	{
		scanf("%d",&a[i]);
		if(a[i] %4 == 0)
		num_4 ++;
		else if(a[i] % 2 == 0)
		num_2 ++;
	}
	if(num_4 + num_2/2 >= n/2)
	flag = 1;
    printf("%s\n",flag?"Yes":"No");
}