You are given a $2$D integer array towers where each towers[i] = $[x_i, y_i, q_i]$ denotes a tower located at coordinates $(x_i, y_i)$ with a quality factor $q_i$. You are also given an integer array center = $[cx, cy]$ representing a location and an integer radius.

A tower is considered reachable if the Manhattan distance between $(x_i, y_i)$ and $(cx, cy)$ is at most radius. The Manhattan distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $|x_1 - x_2| + |y_1 - y_2|$.

Return an integer array $[x, y]$ representing the coordinates of the reachable tower with the maximum quality factor. If multiple reachable towers share the same maximum quality factor, return the one with the lexicographically smallest coordinate. If no tower is reachable, return $[ -1, -1 ]$.

Note: A coordinate $[x_1, y_1]$ is lexicographically smaller than $[x_2, y_2]$ if $x_1 < x_2$, or if $x_1 = x_2$ and $y_1 < y_2$.

Constraints:

• $1 \leq$ towers.length $\leq 10^5$

• towers[i] = $[x_i, y_i, q_i]$

• center = $[cx, cy]$

• $0 \leq x_i, y_i, q_i, cx, cy \leq 10^5$

• $0 \leq$ radius $\leq 10^5$

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.