<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 sol(int sx,int sy,int dx,int dy,int n,int m,string &visi,string s){
        if(sx==dx && sy==dy){
            if(s!=visi){
                return 0;
            }
            else{
                return 1;
            }
        }
        int sum=0;
        // cout<<visi<<" "<<s<<endl;
        // cout<<sx<<" "<<sy<<endl;
        if(sx-1>=0){
            if(visi[(sx-1)*m+sy]=='1' && s[(sx-1)*m+sy]=='0'){
                s[(sx-1)*m+sy]='1';
            sum=sum+sol(sx-1,sy,dx,dy,n,m,visi,s);
            s[(sx-1)*m+sy]='0';
            }
        }
        if(sy-1>=0){
            if(visi[(sx)*m+sy-1]=='1' && s[(sx)*m+sy-1]=='0'){
                s[(sx)*m+sy-1]='1';
            sum=sum+sol(sx,sy-1,dx,dy,n,m,visi,s);
            s[(sx)*m+sy-1]='0';
            }
        }
        if(sx+1 < n){
            if(visi[(sx+1)*m+sy]=='1' && s[(sx+1)*m+sy]=='0'){
                s[(sx+1)*m+sy]='1';
            sum=sum+sol(sx+1,sy,dx,dy,n,m,visi,s);
            s[(sx+1)*m+sy]='0';
            }
        }
        if(sy+1 < m){
            if(visi[(sx)*m+sy+1]=='1' && s[(sx)*m+sy+1]=='0'){
                s[(sx)*m+sy+1]='1';
            sum=sum+sol(sx,sy+1,dx,dy,n,m,visi,s);
            s[(sx)*m+sy+1]='0';
            }
        }
        return sum;
    }



    int uniquePathsIII(vector<vector<int>>& grid) {
        string visi="";
        int sx,sy,dx,dy;
        int n=grid.size();
        int m=grid[0].size();
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(grid[i][j]==0){
                    visi.push_back('1');
                }
                else if(grid[i][j]==1){
                    visi.push_back('1');
                    sx=i;
                    sy=j;
                }
                else if(grid[i][j]==2){
                    visi.push_back('1');
                    dx=i;
                    dy=j;
                }
                else{
                    visi.push_back('0');
                }
            }
        }
        string s="";
        for(int i=0;i<n*m;i++){
            if(i==(sx*m+sy)){
                s.push_back('1');
            }
            else{
                s.push_back('0');
            }
        }
        return sol(sx,sy,dx,dy,n,m,visi,s);
    }
};
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