<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 {
private:
    int ans = 0;
    pair<int,int> steps[4] = {{1,0},{-1,0},{0,1},{0,-1}};
    bool valid(int x, int y, vector<vector<int>>& grid, vector<vector<int>> vis){
        int n = grid.size(); int m = grid[0].size();
        if(x>=0 && x<n && y>=0 && y<m){
            if(grid[x][y]!=-1 && vis[x][y]==0) return true;
        }
        return false;
    }
    bool check(vector<vector<int>>& grid, vector<vector<int>> vis){
        for(int i=0; i<grid.size(); i++){
            for(int j=0; j<grid[0].size(); j++){
                if(grid[i][j]!=-1){
                    if(!vis[i][j]) return false;
                }
            }
        }
        return true;
    }

    void rec(int x, int y, vector<vector<int>>& grid, vector<vector<int>> vis, int z1, int z2){
        //cout<<x<<" "<<y<<"\n";
        vis[x][y]=1;
        if(x==z1 && y==z2) { 
            if(check(grid,vis)) ans++; 
            return; 
        }
        for(auto v: steps){
            int a = x+v.first;
            int b = y+v.second;
            if(valid(a,b,grid,vis)) rec(a,b,grid,vis,z1,z2);
        }
        return;
    }
public:
    int uniquePathsIII(vector<vector<int>>& grid) {
        ans = 0;
        vector<vector<int>> vis(grid.size(), vector<int>(grid[0].size(), 0));
        pair<int,int> st, en;
        for(int i=0; i<grid.size(); i++) for(int j=0; j<grid[0].size(); j++) { 
            if(grid[i][j]==1) st={i,j};
            if(grid[i][j]==2) en={i,j};
        }
        rec(st.first,st.second,grid,vis,en.first,en.second);
        return ans;
    }
};
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