There are n points positioned along a road, numbered from $1$ to n. You are given the integer n and a $2 ext{D}$ integer array rides, where rides[i] = [start_i, end_i, tip_i] indicates that the $i^{ ext{th}}$ passenger wants to travel from point start_i to point end_i and will provide a tip of tip_i dollars.

If you choose to transport passenger $i$, you earn (end_i $-$ start_i $+$ tip_i) dollars. You can only carry at most $1$ passenger at any given time. You can only move forward from smaller numbered points to larger numbered points. Dropping off a passenger at a point allows you to immediately pick up another passenger at that same point.

Return the maximum total earnings you can collect.

Constraints:

• $1 \le$ n $\le 10^5$

• $1 \le$ rides.length $\le 3 imes 10^4$

• rides[i].length $= 3$

• $1 \le$ start_i $<$ end_i $\le$ n

• $1 \le$ tip_i $\le 10^5$

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.