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 alcout=0,a2count=0,a4count=0;
	int i,N,x;
	
	scanf("%d",&N);
	while(N--)
	{
		scanf("%d",&x);
		if(x%4==0)
			a4count++;
		else if(x%2==0)	
			a2count++;
		else
			a1count++;	
	}
	
	if(a2count>0 &&a1count<=a4count)
		printf("Yes\n");
	else if(a2count==0 && a1count<=a4count+1)	
		printf("Yes\n");
	else
		printf("N0\n");
}