<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 c = 0, sum=2;
    int endx, endy;
    void func(vector<vector<int>>& nums, int x, int y, vector<vector<int>>& sol) {
        if (x < 0 || y < 0 || x >= nums.size() || y >= nums[0].size() || nums[x][y] == -1 || sol[x][y] == 1) {
            return;
        }
        
        if (x == endx && y == endy) {
            int s = 0;
            sol[x][y] = 1;
            for(auto i: sol) {
                for(int j: i)
                    if(j == 1)
                        s++;
            }
            if(s == sum)
                c++;
            sol[x][y] = 0;
            return;
        }

        if(nums[x][y] != -1) {
            sol[x][y] = 1; 
            func(nums, x + 1, y, sol); 
            func(nums, x, y + 1, sol); 
            func(nums, x-1, y , sol); 
            func(nums, x, y - 1, sol); 
            sol[x][y] = 0; 
        }
    }

    int uniquePathsIII(vector<vector<int>>& nums) {
        vector<vector<int>> sol(nums.size(), vector<int>(nums[0].size(), 0));
        int sx, sy;
        for(int i=0; i<nums.size(); i++) {
            for(int j=0; j<nums[0].size(); j++)
                if(nums[i][j] == 1) {
                    sx = i;
                    sy = j;
                } else if(nums[i][j] == 2) {
                    endx = i;
                    endy = j;
                } else if(nums[i][j] != -1) {
                    sum++;
                }
        }
        func(nums, sx, sy, sol);
        return c;
    }
};
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