Simulate rover movement on a grid

You are building a rover navigation simulator. ## Part 1: Single rover on a 2D map You are given: - A rectangular 2D grid with coordinates `(x, y)`. - A rover starting position `(x0, y0)` and a facing direction (one of `N, E, S, W`). - A command string consisting of: - `L`: turn left 90° - `R`: turn right 90° - `M`: move forward 1 step in the current facing direction Rules: - The rover cannot move outside the map boundaries. If a command would move it out of bounds, ignore that move (or alternatively, return an error—state your chosen behavior clearly and implement it consistently). Task: Implement a function that returns the rover’s final position and direction after executing all commands. ## Part 2: Multiple rovers Extend the design to support multiple rovers on the same 2D map. - Each rover has its own initial state and command string. - (Clarify your assumption) Either rovers execute sequentially (one after another) or simultaneously step-by-step. - Decide and implement a collision policy (e.g., rovers cannot occupy the same cell; a move that would collide is rejected). Task: Explain how you would change the code structure/API to support multiple rovers cleanly and safely. ## Part 3: 3D map Now the map is 3D with coordinates `(x, y, z)`. - Define a reasonable model for orientation in 3D (e.g., a heading direction plus pitch, or facing as one of 6 axes: `+X, -X, +Y, -Y, +Z, -Z`). - Extend commands accordingly (you may introduce new commands if needed, but specify them). Task: Describe and/or implement how your solution generalizes to 3D while keeping the design maintainable.