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

A pair of points (A, B) is considered valid if:

• Point A is to the upper left of point B, meaning A[0] $\leq$ B[0] and A[1] $\geq$ B[1].

• No other point C lies inside or on the border of the rectangle formed with A as its upper left corner and B as its lower right corner. That is, there is no point C other than A and B such that A[0] $\leq$ C[0] $\leq$ B[0] and B[1] $\leq$ C[1] $\leq$ A[1].

Return the total number of valid pairs (A, B).

Constraints:

• $2 \leq$ n $\leq 50$, where n == points.length

• points[i].length $= 2$

• $0 \leq$ points[i][0], points[i][1] $\leq 50$

• All elements in points are 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.