A robot starts on an infinite $XY$ plane at coordinates $(0, 0)$ facing north. It receives an array of integers commands, representing a sequence of actions:

• $-2$: Turn left $90$ degrees.

• $-1$: Turn right $90$ degrees.

• $k$ (where $1 \le k \le 9$): Move forward $k$ units, one unit at a time.

There are obstacles on the grid, provided in an array obstacles where each element obstacles[i] $= [x_i, y_i]$ denotes the coordinates of an obstacle. If the robot encounters an obstacle while moving, it stops in the cell immediately before the obstacle and continues with the next command.

Return the maximum squared Euclidean distance from the origin that the robot reaches at any point along its path.

Note: The squared Euclidean distance of a position $(x, y)$ from the origin $(0, 0)$ is defined as $x^2 + y^2$.

Constraints:

• $1 \le$ commands.length $\le 10^4$

• commands[i] is either $-2$, $-1$, or an integer in the range $[1, 9]$

• $0 \le$ obstacles.length $\le 10^4$

• $-3 \times 10^4 \le x_i, y_i \le 3 \times 10^4$

• The answer is guaranteed to be less than $2^{31}$

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.