You are given a $2$D integer array tasks, where tasks[i] = [start_i, end_i, duration_i].

Each task must be actively run for a total of duration_i integer time units within the inclusive time interval $[$start_i, end_i$]$.

The computer can run multiple tasks simultaneously, and running several tasks during the same time unit only counts as $1$ unit of active time.

Return the minimum total time units the computer must be turned on to complete all tasks.

Constraints:

• $1 \leq$ tasks.length $\leq 2000$

• tasks[i].length $= 3$

• $1 \leq$ start_i, end_i $\leq 2000$

• $1 \leq$ duration_i $\leq$ end_i $-$ start_i $+ 1$

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.