<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 {
    int ans=0,L=0,R,C;
public:
    void util(int i,int j,int& len,vector<vector<bool>>& visited,vector<vector<int>>& grid){
        function<bool(int,int)> valid=[&](int i,int j){
            if(i<0 || i>=R || j<0 ||j>=C) return false;
            return true;
        };
        if(len==L && grid[i][j]==2) {ans++; return;}
        for(vector<int> p:vector<vector<int>>{{-1,0},{0,-1},{1,0},{0,1}}){
            int i1=i+p[0],j1=j+p[1];
            if(valid(i1,j1) && grid[i1][j1]!=-1 && !visited[i1][j1] ){
                visited[i1][j1]=true;
                len++;
                util(i1,j1,len,visited,grid);
                len--;
                visited[i1][j1]=false;
            }
        } 
    }    

    int uniquePathsIII(vector<vector<int>>& grid) {
         R=grid.size(),C=grid[0].size();
         int s_i,s_j;
        for(int i=0;i<R;i++){
            for(int j=0;j<C;j++){
                if(grid[i][j]==0 || grid[i][j]==2) L++;
                else if(grid[i][j]==1) {s_i=i; s_j=j;} 
            }
        }
        // cout<<s_i<<" "<<s_j<<" "<< L<<endl;
        int len=0;
        vector<vector<bool>> visited(R,vector<bool>(C,false));
        visited[s_i][s_j]=true;
        util(s_i,s_j,len, visited, grid);
        return ans; 

    }
};
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