<p>Given an <code>m x n</code> integer matrix <code>heightMap</code> representing the height of each unit cell in a 2D elevation map, return <em>the volume of water it can trap after raining</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/08/trap1-3d.jpg" style="width: 361px; height: 321px;" />
<pre>
<strong>Input:</strong> heightMap = [[1,4,3,1,3,2],[3,2,1,3,2,4],[2,3,3,2,3,1]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> After the rain, water is trapped between the blocks.
We have two small ponds 1 and 3 units trapped.
The total volume of water trapped is 4.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/08/trap2-3d.jpg" style="width: 401px; height: 321px;" />
<pre>
<strong>Input:</strong> heightMap = [[3,3,3,3,3],[3,2,2,2,3],[3,2,1,2,3],[3,2,2,2,3],[3,3,3,3,3]]
<strong>Output:</strong> 10
</pre>

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

<ul>
	<li><code>m == heightMap.length</code></li>
	<li><code>n == heightMap[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 200</code></li>
	<li><code>0 &lt;= heightMap[i][j] &lt;= 2 * 10<sup>4</sup></code></li>
</ul>

class Solution:
    def trapRainWater(self, heightMap: List[List[int]]) -> int:
        heap, seen = [], set()
        for y in range(len(heightMap)):
            for x in range(len(heightMap[0])):
                if y in [0, len(heightMap) - 1] or x in [0, len(heightMap[0]) - 1]:
                    heapq.heappush(heap, (heightMap[y][x], y, x))
                    seen.add((y, x))
                
        total, level = 0, 0

        while heap:
            h, y, x = heapq.heappop(heap)
            level = max(level, h)
            
            for dy, dx in [(1, 0), (-1, 0), (0, 1), (0, -1)]:
                yy, xx = y + dy, x + dx
                if 0 <= yy < len(heightMap) and 0 <= xx < len(heightMap[0]) and (yy, xx) not in seen:
                    heapq.heappush(heap, (heightMap[yy][xx], yy, xx))
                    total += max(0, level - heightMap[yy][xx])
                    seen.add((yy, xx))

        return total 

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