<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:
    directions = [[1,0], [-1,0], [0, 1], [0, -1]]
    capacity = 0

    def getMaximumGold(self, grid: List[List[int]]) -> int:
        rows, cols = len(grid), len(grid[0])

        for row in range (rows):
            for col in range (cols):
                if grid[row][col] != 0:
                    self.capacity = max(self.capacity, self.backtrack(grid, row, col, rows, cols))
        
        return self.capacity

    def backtrack(self, grid: List[List[int]], row: int, col: int, rows: int, cols: int) -> int:
        # check boundary
        if row<0 or col<0 or row>=rows or col>=cols or grid[row][col] == 0:
            return 0

        curr = grid[row][col]
        grid[row][col] = 0
        localMaxGold = curr

        for i in range(len(self.directions)):
            newRow = row + self.directions[i][0]
            newCol = col + self.directions[i][1]
            localMaxGold = max(localMaxGold, curr + self.backtrack(grid, newRow, newCol, rows, cols))

        grid[row][col] = curr

        return localMaxGold


16600