<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:
        rows, cols = len(heightMap), len(heightMap[0])
        heap = []
        visited = set()
        for i in range(rows):
            heapq.heappush(heap, (heightMap[i][0], i, 0))
            heapq.heappush(heap, (heightMap[i][cols-1], i, cols-1))
            visited.add((i, 0))
            visited.add((rows-1-i, 0))
        for j in range(1,cols-1):
            heapq.heappush(heap, (heightMap[0][j], 0, j))
            heapq.heappush(heap, (heightMap[rows-1][j], rows-1, j))
            visited.add((0, j))
            visited.add((0, cols-1-j))
        templist = []
        level = 1
        total = 0

        def visit(r, c, level, t):
            if r < 0 or r >= rows or c < 0 or c >= cols or (r,c) in visited:
                return t
            visited.add((r, c))
            if r > 0 and r < rows-1 and c > 0 and c < cols -1 and heightMap[r][c] < level:
                print("adding to total: ", heightMap[r][c], r, c)
                t += level - heightMap[r][c]
            heapq.heappush(heap, (heightMap[r][c], r, c))
            return t
        
        while heap:
            print("level = ", level)
            while heap and heap[0][0] <= level:
                height, r, c = heapq.heappop(heap)
                print(r,",",c)
                total = visit(r-1, c, level, total)
                total = visit(r+1, c, level, total)
                total = visit(r, c-1, level, total)
                total = visit(r, c+1, level, total)
            level += 1
        
        return total


23700