<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 {
public:
    bool valid(int x,int y,int n,int m){
        if(x<n&&y<m&&x>=0&&y>=0)return true;
        return false;
    }
    int trapRainWater(vector<vector<int>>& k) {
        int n=k.size();
        int m=k[0].size();
        set<vector<int>>s;
        vector<vector<bool>>vis(n, vector<bool>(m,false));
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(i==0||j==0||i==n-1||j==m-1)s.insert({k[i][j],i,j}),vis[i][j]=true;
            }
        }int ans=0;
        while(s.size()){
            vector<int>sm=(*s.begin());
            s.erase(s.begin());
            int x=sm[1];int y=sm[2];
            int val=sm[0];
           
            for(int i=-1;i<=1;i++){
                for(int j=-1;j<=1;j++){
                    if(abs(i)==abs(j))continue;
                    int x1=x+i;int y1=y+j;
                    if(valid(x1,y1,n,m)&&vis[x1][y1]==false){
                        if(val<=k[x1][y1])s.insert({k[x1][y1],x1,y1});
                        else ans+=val-k[x1][y1],s.insert({val,x1,y1});
                        vis[x1][y1]=true;
                    }
                }
            }
        }return ans;
    }
};
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