Escape Room (Shortest Escape Path in a Room Grid)

Problem You are given a 2D grid representing an escape room. Your character starts at cell S and must reach the exit E in the fewest possible steps, obeying the rules below. Cell types Each cell contains one of these characters: S – start (appears exactly once) E – exit (appears exactly once) . – empty floor # – wall (impassable) a–z – keys; stepping onto the cell automatically picks up the key A–Z – doors; you may enter a door only if you already hold the matching lowercase…