<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 {
private:
    int go(int i, int j, vector<vector<int>>& grid, int& val) {
        if (i >= grid.size() || i < 0 || j >= grid[0].size() || j < 0)
            return val;

        if (val > grid[i][j])
            return val - grid[i][j];

        return 0;
    }

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

        int area = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (grid[i][j]) {
                    area += 2;
                    area += go(i - 1, j, grid, grid[i][j]);
                    area += go(i + 1, j, grid, grid[i][j]);
                    area += go(i, j - 1, grid, grid[i][j]);
                    area += go(i, j + 1, grid, grid[i][j]);
                }
                    
            }
        }

        return area;
    }
};

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