Valid Square

Statement

Given the coordinates of four points $P_1$, $P_2$, $P_3$, and $P_4$ in 2D space, determine if these points form a square.

Each point $P_i$ is represented as $[x_i,\space y_i]$, and the points may be provided in any order.

A square is defined as having:

• Four sides of equal positive length

• Four right angles (90 degrees)

Constraints:

• p1.length == p2.length == p3.length == p4.length == 2

• $-10^4\leq$ $x_i, \space y_i$ $\leq 10^4$

Examples