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

Return the total number of distinct horizontal trapezoids that can be formed using $4$ points from points.

A horizontal trapezoid is a quadrilateral with at least one pair of parallel horizontal sides (parallel to the $X$ axis). That is, its $4$ vertices must consist of $2$ distinct points sharing a common $y$ coordinate and $2$ distinct points sharing a different common $y$ coordinate.

Constraints:

• $4 \leq$ points.length $\leq 10^5$

• $-10^8 \leq x_i, y_i \leq 10^8$

• All points are pairwise distinct.

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.