<p>You are given an <code>m x n</code> integer array <code>grid</code> where <code>grid[i][j]</code> could be:</p> <ul> <li><code>1</code> representing the starting square. There is exactly one starting square.</li> <li><code>2</code> representing the ending square. There is exactly one ending square.</li> <li><code>0</code> representing empty squares we can walk over.</li> <li><code>-1</code> representing obstacles that we cannot walk over.</li> </ul> <p>Return <em>the number of 4-directional walks from the starting square to the ending square, that walk over every non-obstacle square exactly once</em>.</p> <p> </p> <p><strong class="example">Example 1:</strong></p> <img alt="" src="https://assets.leetcode.com/uploads/2021/08/02/lc-unique1.jpg" style="width: 324px; height: 245px;" /> <pre> <strong>Input:</strong> grid = [[1,0,0,0],[0,0,0,0],[0,0,2,-1]] <strong>Output:</strong> 2 <strong>Explanation:</strong> We have the following two paths: 1. (0,0),(0,1),(0,2),(0,3),(1,3),(1,2),(1,1),(1,0),(2,0),(2,1),(2,2) 2. (0,0),(1,0),(2,0),(2,1),(1,1),(0,1),(0,2),(0,3),(1,3),(1,2),(2,2) </pre> <p><strong class="example">Example 2:</strong></p> <img alt="" src="https://assets.leetcode.com/uploads/2021/08/02/lc-unique2.jpg" style="width: 324px; height: 245px;" /> <pre> <strong>Input:</strong> grid = [[1,0,0,0],[0,0,0,0],[0,0,0,2]] <strong>Output:</strong> 4 <strong>Explanation:</strong> We have the following four paths: 1. (0,0),(0,1),(0,2),(0,3),(1,3),(1,2),(1,1),(1,0),(2,0),(2,1),(2,2),(2,3) 2. (0,0),(0,1),(1,1),(1,0),(2,0),(2,1),(2,2),(1,2),(0,2),(0,3),(1,3),(2,3) 3. (0,0),(1,0),(2,0),(2,1),(2,2),(1,2),(1,1),(0,1),(0,2),(0,3),(1,3),(2,3) 4. (0,0),(1,0),(2,0),(2,1),(1,1),(0,1),(0,2),(0,3),(1,3),(1,2),(2,2),(2,3) </pre> <p><strong class="example">Example 3:</strong></p> <img alt="" src="https://assets.leetcode.com/uploads/2021/08/02/lc-unique3-.jpg" style="width: 164px; height: 165px;" /> <pre> <strong>Input:</strong> grid = [[0,1],[2,0]] <strong>Output:</strong> 0 <strong>Explanation:</strong> There is no path that walks over every empty square exactly once. Note that the starting and ending square can be anywhere in the grid. </pre> <p> </p> <p><strong>Constraints:</strong></p> <ul> <li><code>m == grid.length</code></li> <li><code>n == grid[i].length</code></li> <li><code>1 <= m, n <= 20</code></li> <li><code>1 <= m * n <= 20</code></li> <li><code>-1 <= grid[i][j] <= 2</code></li> <li>There is exactly one starting cell and one ending cell.</li> </ul>