You are given a $2 ext{D}$ integer array points, where points[i] $= [x_i, y_i]$ represents the coordinates of distinct points on a $2 ext{D}$ plane.

Two points are connected if they share the same $x$ coordinate or the same $y$ coordinate.

You may choose any coordinate $(x, y)$ on the plane, add a new point at that location, and activate it. When a point is activated, any unactivated point that shares an $x$ coordinate or a $y$ coordinate with an already activated point also becomes activated in a chain reaction.

Return the maximum total number of points, including the newly added point, that can be activated.

Constraints:

• $1 \leq$ points.length $\leq 10^5$

• points[i] $= [x_i, y_i]$

• $-10^9 \leq x_i, y_i \leq 10^9$

• points contains all distinct coordinates.

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.