You are given three integer arrays robots, distance, and walls, all representing positions on a $1\text{D}$ number line.

There are $n$ robots, where the $i^{\text{th}}$ robot is located at position robots[i] and has a maximum firing range of distance[i]. Each robot can choose to fire a laser beam either to the left or to the right:

• If robot $i$ fires to the left, the beam covers the interval $[\max(\text{left\_bound}, \text{robots}[i] - \text{distance}[i]), \text{robots}[i]]$, where $\text{left\_bound}$ is the position of the nearest robot to its left plus $1$, or $-\infty$ if no such robot exists.

• If robot $i$ fires to the right, the beam covers the interval $[\text{robots}[i], \min(\text{right\_bound}, \text{robots}[i] + \text{distance}[i])]$, where $\text{right\_bound}$ is the position of the nearest robot to its right minus $1$, or $+\infty$ if no such robot exists.

A laser beam cannot pass through another robot. Any wall located within the covered range of a laser beam is destroyed.

Return the maximum number of unique walls that can be destroyed if each robot independently chooses to fire either to the left or to the right.

Constraints:

• $1 \leq$ robots.length $=$ distance.length $\leq 10^5$

• $1 \leq$ walls.length $\leq 10^5$

• $1 \leq$ robots[i], walls[j] $\leq 10^9$

• $1 \leq$ distance[i] $\leq 10^5$

• All values in robots are unique.

• All values in walls are unique.

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.