There are n distinct virus variants located on a $2$D integer grid. You are given a $2$D integer array points of size n, where points[i] $= [x_i, y_i]$ represents the initial location of the $i$-th virus variant at day $0$, and an integer k.

Each day, every virus variant spreads by $1$ unit in Manhattan distance in all directions. Thus, on day $d$, the $i$-th virus variant will have spread to all integer coordinate points $(x, y)$ satisfying:

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.