593. Valid Square

Medium

30 Points

Math

Geometry

Given the coordinates of four points in 2D space p1, p2, p3 and p4, return true if the four points construct a square. The coordinate of a point pi is represented as [xi, yi]. The input is not given in any order. A valid square has four equal sides with positive length and four equal angles (90-degree angles).

Examples

Example 1

Input: p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,1] Output: true

Example 2

Input: p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,12] Output: false

Example 3

Input: p1 = [1,0], p2 = [-1,0], p3 = [0,1], p4 = [0,-1] Output: true

Constraints

p1.length == p2.length == p3.length == p4.length == 2
-104 <= xi, yi <= 104