<p>In a gold mine <code>grid</code> of size <code>m x n</code>, each cell in this mine has an integer representing the amount of gold in that cell, <code>0</code> if it is empty.</p>

<p>Return the maximum amount of gold you can collect under the conditions:</p>

<ul>
	<li>Every time you are located in a cell you will collect all the gold in that cell.</li>
	<li>From your position, you can walk one step to the left, right, up, or down.</li>
	<li>You can&#39;t visit the same cell more than once.</li>
	<li>Never visit a cell with <code>0</code> gold.</li>
	<li>You can start and stop collecting gold from <strong>any </strong>position in the grid that has some gold.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> grid = [[0,6,0],[5,8,7],[0,9,0]]
<strong>Output:</strong> 24
<strong>Explanation:</strong>
[[0,6,0],
 [5,8,7],
 [0,9,0]]
Path to get the maximum gold, 9 -&gt; 8 -&gt; 7.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,0,7],[2,0,6],[3,4,5],[0,3,0],[9,0,20]]
<strong>Output:</strong> 28
<strong>Explanation:</strong>
[[1,0,7],
 [2,0,6],
 [3,4,5],
 [0,3,0],
 [9,0,20]]
Path to get the maximum gold, 1 -&gt; 2 -&gt; 3 -&gt; 4 -&gt; 5 -&gt; 6 -&gt; 7.
</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;= 15</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 100</code></li>
	<li>There are at most <strong>25 </strong>cells containing gold.</li>
</ul>

class Solution {
public:

    bool isValid(int row,int col,vector<vector<int>>&vis,vector<vector<int>>&grid,int n, int m){
        if(row>=0&&col>=0&&row<n&&col<m&&vis[row][col]==0&&grid[row][col]!=0) return true;
        return false;
    }

    void getGold(int row,int col,int sum,vector<vector<int>>&grid,vector<vector<int>>&vis,vector<int>& ans,vector<char>&ch,int n,int m){
                    ans.push_back(sum);
            for(auto c:ch){
                if(c=='d'&&isValid(row+1,col,vis,grid,n,m)){
                    vis[row+1][col]=1;
                    sum+=grid[row+1][col];
                    getGold(row+1,col,sum,grid,vis,ans,ch,n,m);
                    vis[row+1][col]=0;
                    sum-=grid[row+1][col];
                }
                else if(c=='l'&&isValid(row,col-1,vis,grid,n,m)){
                    vis[row][col-1]=1;
                    sum+=grid[row][col-1];
                    getGold(row,col-1,sum,grid,vis,ans,ch,n,m);
                    vis[row][col-1]=0;
                    sum-=grid[row][col-1];
                }
                else if(c=='r'&&isValid(row,col+1,vis,grid,n,m)){
                    vis[row][col+1]=1;
                    sum+=grid[row][col+1];
                    getGold(row,col+1,sum,grid,vis,ans,ch,n,m);
                    vis[row][col+1]=0;
                    sum-=grid[row][col+1];
                }
                else if(c=='u'&&isValid(row-1,col,vis,grid,n,m)){
                    vis[row-1][col]=1;
                    sum+=grid[row-1][col];
                    getGold(row-1,col,sum,grid,vis,ans,ch,n,m);
                    vis[row-1][col]=0;
                    sum-=grid[row-1][col];
                }
            

             
                }
            }
      

    

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

        vector<vector<int>>vis(n,vector<int>(m,0));
        vector<int> ans;

        vector<char> ch={'d','l','r','u'};
        int flag=0;
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
            if(grid[i][j]!=0) flag=1;
            if(grid[i][j]!=0){
            vis[i][j]=1;
            getGold(i,j,grid[i][j],grid,vis,ans,ch,n,m);   
            vis[i][j]=0;             
            }

            }
        }

        if(flag==0) return 0;

        return *max_element(ans.begin(),ans.end());
    }
};
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