Unique Paths III

Statement

You are given a  $m \times n$  integer array, grid, where each cell, grid[i][j], can have one of the following values:

• 1 indicates the starting point. There is exactly one such square.

• 2 marks the ending point. There is exactly one such square.

• 0 represents empty squares that can be walked over.

• -1 represents obstacles that cannot be crossed.

Your task is to return the total number of unique four-directional paths from the starting square (1) to the ending square (2), such that every empty square is visited exactly once during the walk.

Constraints:

• ...