<p>You are given an <code>n x n</code> <code>grid</code> where you have placed some <code>1 x 1 x 1</code> cubes. Each value <code>v = grid[i][j]</code> represents a tower of <code>v</code> cubes placed on top of cell <code>(i, j)</code>.</p>

<p>After placing these cubes, you have decided to glue any directly adjacent cubes to each other, forming several irregular 3D shapes.</p>

<p>Return <em>the total surface area of the resulting shapes</em>.</p>

<p><strong>Note:</strong> The bottom face of each shape counts toward its surface area.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/08/tmp-grid2.jpg" style="width: 162px; height: 162px;" />
<pre>
<strong>Input:</strong> grid = [[1,2],[3,4]]
<strong>Output:</strong> 34
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/08/tmp-grid4.jpg" style="width: 242px; height: 242px;" />
<pre>
<strong>Input:</strong> grid = [[1,1,1],[1,0,1],[1,1,1]]
<strong>Output:</strong> 32
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/08/tmp-grid5.jpg" style="width: 242px; height: 242px;" />
<pre>
<strong>Input:</strong> grid = [[2,2,2],[2,1,2],[2,2,2]]
<strong>Output:</strong> 46
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == grid.length == grid[i].length</code></li>
	<li><code>1 &lt;= n &lt;= 50</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 50</code></li>
</ul>

class Solution:
    def surfaceArea(self, grid):
        n = len(grid)
        total_area = 0
        
        for i in range(n):
            for j in range(n):
                # Get the number of cubes in the current cell
                height = grid[i][j]
                
                if height > 0:
                    # Each cell contributes 4 vertical faces and 2 horizontal (top and bottom) faces
                    total_area += height * 4 + 2
                
                    # Subtract overlapping faces with adjacent cells
                    if i > 0:
                        total_area -= min(height, grid[i - 1][j]) * 2
                    if j > 0:
                        total_area -= min(height, grid[i][j - 1]) * 2
        
        return total_area

16500