You are given a two dimensional array points of size n, where points[i] = [x_i, y_i] represents the coordinates of the $i^{ ext{th}}$ person on a Cartesian plane.

You need to select a pair of distinct people, placing Alice at point $A = (x_A, y_A)$ and Bob at point $B = (x_B, y_B)$, such that:

• Alice is at the upper left position relative to Bob, meaning $x_A \leq x_B$ and $y_A \geq y_B$.

• No other person is located strictly inside or on the boundary of the rectangular region defined by Alice and Bob as opposite corners. Specifically, there is no third person at point $C = (x_C, y_C)$ such that $x_A \leq x_C \leq x_B$ and $y_B \leq y_C \leq y_A$.

Return the total number of valid pairs of people $(A, B)$ that can be chosen.

Note: The rectangular region may have an area of $0$, which occurs when $x_A = x_B$ or $y_A = y_B$.

Constraints:

• $2 \leq$ n $\leq 1000$, where n is the length of points

• points[i].length $= 2$

• $-10^9 \leq$ points[i][0], points[i][1] $\leq 10^9$

• All points[i] 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.