Check Square

You are given four points on a two-dimensional coordinate system.

Can you check if those four points make a square?

Example:

Let the input be [1,0,2,1] and [0,1,1,2].
So, the coordinates of the four points be [ {1, 0}, {0, 1}, {2, 1}, {1, 2} ]

From the above image, we can see that it is a square. Thus, the output will be ‘Yes’.

Input format:

The first line of input contains an integer ‘T’ denoting the number of test cases.

The first line of each test case contains four space-separated integers representing x-coordinates of the four points.

The second line of each test case contains four space-separated integers representing y-coordinates of the four points.

Output format :

For each test case, print ‘Yes’ if four points make a square otherwise print ‘No’.

Note:

Don’t print anything, just return True if four points make a square otherwise return False.

Constraints:

1 <= T <= 10^4
-10^9 <= xi, yi <= 10^9

Time limit: 1 sec

Sample Input 1:

2
1 0 2 1
0 1 1 2
1 0 0 1
1 0 1 2

Sample Output 1:

Yes
No

Explanation For Sample Input 1:

Test Case 1: Refer to the example described above.

Test Case 2:
    The quadrilateral for the given four points is represented below.

As we can clearly see this is not a square. Thus, the answer will be ‘No’.

Sample Input 2:

2
1 2 4 2
0 2 4 2
0 1 2 3
1 -1 2 0

Sample Output 2:

No
Yes