Tallest building between parking lots

A city block is drawn as a rectangular grid of strings. Each tile is one of:

• 'P': a parking lot. Its height is fixed at 0.
• '-': a lot where a building can go. You choose its height (a non-negative integer).
• 'X': unusable land. Nothing is built there and it imposes no rule.

Zoning rule: any two usable tiles ('P' or '-') that share an edge (up, down, left, right; not diagonal) may differ in height by at most 1.

Implement:

def max_building_height(grid: list[str]) -> int: ...

Return the height of the tallest building that can legally be placed anywhere on the grid, assuming every building is made as tall as the rule allows. Return -1 if some building tile cannot reach any parking lot through usable tiles (its height would be unbounded). If the grid has no building tiles, return 0.

Constraints: 0 <= rows, cols <= 1000; the grid is rectangular. Aim for time linear in the number of tiles.

Example 1

P--
---
--P

Answer: 2. The tiles at (0,2), (1,1) and (2,0) are each two steps from the nearest lot.

Example 2

P-X--
--X-P

Answer: 2. The X column splits the block in two; each half has its own lot, and the farthest building on either side is two steps away.

Example 3

PX-

Answer: -1. The building on the right is walled off from every lot.

Follow-up: also return the full grid of maximum heights.