<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:
        m,n=len(heightMap),len(heightMap[0])
        if m<3 or n<3:
            return 0
        def adjacent(i,j):
            return [(i-1,j),(i+1,j),(i,j-1),(i,j+1)]
        d=defaultdict(list)
        for i  in range(m):
            for j in range(n):
                d[heightMap[i][j]].append((i,j))
        heights=sorted(d.items())
        volume,area,lowerH=0,0,heights[0][0]
        level=[[1 for j in range(n)] for i in range(m)]
        for h,position in heights:
            volume+=area*(h-lowerH)
            lowerH=h
            leak=[]
            for i,j in position:
                level[i][j]=0
                area+=1
                if i==0 or i==m-1 or j==0 or j==n-1 or any([level[a][b] == -1 for a, b in adjacent(i,j)]):
                    leak.append((i,j))
                    level[i][j]=-1
                    area-=1
            while leak:
                i,j=leak.pop()
                for a,b in adjacent(i,j):
                    if 0<=a<m and 0<=b<n and not level[a][b]:
                        leak.append((a,b))
                        level[a][b]=-1
                        area-=1
        return volume
21800