Maze Runner Challenge

You are given a 2D grid of integers representing a maze. Each cell in the grid can be:

• -1: Represents a wall, meaning you cannot move through this cell.
• 0: Represents an open space with no coins.
• Positive integer: Represents an open space that contains that many coins.

The maze dimensions are m x n, and both m and n are odd numbers. This guarantees there is a unique center cell. You start at the center of the grid, and the coins in the starting cell are collected as soon as you begin.

Your objective is to reach any cell on the boundary of the maze (i.e., any cell in the first row, last row, first column, or last column). You can move in four directions: up, down, left, or right (diagonal moves are not allowed).

Your task is to find a path that escapes the maze using the minimum number of moves. Among all such shortest paths, determine the maximum total coins you can collect. If there is no valid path that leads from the center to any boundary, return -1.

Write a function that accepts the 2D grid as input and returns an integer representing the maximum coins collected along a shortest escape path.

Constraints:

• 1 ≤ m, n ≤ 101 (both m and n are odd numbers).
• The grid is represented as a list of lists of integers.
• The center cell (starting point) is guaranteed to be an open space (i.e., not a wall).

Example:

Consider the following grid (5 x 5):

[ [ 0,  -1,  0,   5,  0 ],
  [ 1,   0,  2,  -1,  0 ],
  [ 0,   3, 10,   1,  0 ],
  [ 0,  -1,  2,   0,  4 ],
  [ 0,   0,  0,   0,  0 ] ]

• The starting cell is the center: grid[2][2] with 10 coins.
• One possible escape path might reach the boundary in the fewest steps while collecting extra coins along the way.

Your solution should determine the maximum coins that can be collected along such a shortest escape route.