Implement A* Maze Search

Implement maze pathfinding in C++. You are given an `m x n` grid where `'.'` is an open cell, `'#'` is a wall, `S` is the start, and `T` is the target. You may move up, down, left, or right, and each move has cost `1`. Use the A* algorithm to find a shortest path from `S` to `T`. Return the minimum distance and one valid shortest path as a list of coordinates. If no path exists, report failure. Your solution should: - use an admissible heuristic, - maintain the data needed to reconstruct the path, - avoid revisiting states unnecessarily, - and analyze time and space complexity.