<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>&nbsp;</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>&nbsp;</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 &lt;= m, n &lt;= 20</code></li>
	<li><code>1 &lt;= m * n &lt;= 20</code></li>
	<li><code>-1 &lt;= grid[i][j] &lt;= 2</code></li>
	<li>There is exactly one starting cell and one ending cell.</li>
</ul>

class Solution {
public:
    int uPRec(vector<vector<int>>& grid, int row, int col, int m, int n, int cntNonObsCell) {

        if (grid[row][col] == 2) {
            if (cntNonObsCell == 0)  
                return 1;
            else
                return 0;  
        }

        int rr[] = {-1, 0, +1, 0};
        int cc[] = {0, +1, 0, -1};

        int ans = 0;

        for (int i = 0; i < 4; i++) {
            int curr_r = row + rr[i];
            int curr_c = col + cc[i];

            if (curr_r >= 0 && curr_r < m && curr_c >= 0 && curr_c < n && grid[curr_r][curr_c] != -1 && grid[curr_r][curr_c] != 3 && grid[curr_r][curr_c] != 1) {

                int temp = grid[curr_r][curr_c];  
                if(temp!=2) grid[curr_r][curr_c] = 3;  
                
                ans += uPRec(grid, curr_r, curr_c, m, n, cntNonObsCell - 1); 
                grid[curr_r][curr_c] = temp;  
            }
        }

        return ans;
    }

    int uniquePathsIII(vector<vector<int>>& grid) {
        int m = grid.size();
        int n = grid[0].size();

        int cntNonObsCell = 0; 
        int startRow = -1, startCol = -1;  

       
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (grid[i][j] == 1) {
                    startRow = i;
                    startCol = j;
                    cout<<111;
                }
                if (grid[i][j] != -1) {
                    cntNonObsCell++;  
                }
            }
        }

        
        return uPRec(grid, startRow, startCol, m, n, cntNonObsCell - 1);  
    }
};

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