You are given a list of four points (x, y). Each point is a tuple

Your task is to write a function which takes an array of points and returns whether they form a square.

If the array doesn't contain 4 points, return False.

All points coordinates are integers.

Squares can be rotated using a random degree.

Examples

((1,1), (3,3), (1,3), (3,1)) -> True
((0, 0), (0,2), (2,0), (2,1)) -> False
([]) -> False

Constraints:

1 <= x, y <= 1000

Note:

Performance does not enforced in this kata.