<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:
        n = len(heightMap)
        m = len(heightMap[0])

        def neighbors(x, y):
            yield x + 1, y
            yield x - 1, y
            yield x, y + 1
            yield x, y - 1
        
        def children(x, y):
            for i, j in neighbors(x, y):
                if n > i >= 0 <= j < m and heightMap[i][j] >= 0:
                    yield heightMap[i][j], i, j

        heap = [(heightMap[i][j], i, j) for i in range(n) for j in (0, m - 1)] + [(heightMap[i][j], i, j) for i in (0, n - 1) for j in range(1, m - 1)]
        heapify(heap)

        mh = r = 0

        while heap:
            h, i, j = heappop(heap)
            if heightMap[i][j] < 0:
                continue
            heightMap[i][j] = -1
            if h < mh:
                r += mh - h
            else:
                mh = h
            for v in children(i, j):
                heappush(heap, v)

        return r


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