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2

Check Square

Difficulty: MEDIUM
Contributed By
Anish De |Level 1
Avg. time to solve
10 min
Success Rate
90%

Problem Statement

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} ]

example

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.

test case 2

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
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