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.