Design a data structure that receives a stream of points on the $X$-$Y$ plane and supports querying the number of axis-aligned squares that can be formed.

Implement the DetectSquares class:

• DetectSquares() initializes the object with an empty set of points.

• void add(int[] point) adds a new point point = [x, y] into the data structure. Duplicate points are permitted and are considered distinct instances.

• int count(int[] point) returns the number of ways to choose $3$ points from the data structure such that, together with the query point = [x, y], they form an axis-aligned square of positive area.

Note: An axis-aligned square has all $4$ sides parallel or perpendicular to the coordinate axes.

Constraints:

• point.length $= 2$

• $0 \leq x, y \leq 1000$

• At most $3000$ calls in total will be made to add and count.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.