<p>You are given an <code>n x n</code> integer matrix <code>grid</code> where each value <code>grid[i][j]</code> represents the elevation at that point <code>(i, j)</code>.</p>

<p>The rain starts to fall. At time <code>t</code>, the depth of the water everywhere is <code>t</code>. You can swim from a square to another 4-directionally adjacent square if and only if the elevation of both squares individually are at most <code>t</code>. You can swim infinite distances in zero time. Of course, you must stay within the boundaries of the grid during your swim.</p>

<p>Return <em>the least time until you can reach the bottom right square </em><code>(n - 1, n - 1)</code><em> if you start at the top left square </em><code>(0, 0)</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/29/swim1-grid.jpg" style="width: 164px; height: 165px;" />
<pre>
<strong>Input:</strong> grid = [[0,2],[1,3]]
<strong>Output:</strong> 3
Explanation:
At time 0, you are in grid location (0, 0).
You cannot go anywhere else because 4-directionally adjacent neighbors have a higher elevation than t = 0.
You cannot reach point (1, 1) until time 3.
When the depth of water is 3, we can swim anywhere inside the grid.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/29/swim2-grid-1.jpg" style="width: 404px; height: 405px;" />
<pre>
<strong>Input:</strong> grid = [[0,1,2,3,4],[24,23,22,21,5],[12,13,14,15,16],[11,17,18,19,20],[10,9,8,7,6]]
<strong>Output:</strong> 16
<strong>Explanation:</strong> The final route is shown.
We need to wait until time 16 so that (0, 0) and (4, 4) are connected.
</pre>

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

<ul>
	<li><code>n == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= n &lt;= 50</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;&nbsp;n<sup>2</sup></code></li>
	<li>Each value <code>grid[i][j]</code> is <strong>unique</strong>.</li>
</ul>

class Solution {
    struct cmp{
        bool operator()(tuple<int,int,int>& a,tuple<int,int,int>& b){
            return get<0>(a) >get<0>(b); 
        }
    };
public:

    int swimInWater(vector<vector<int>>& grid) {
        int N=grid.size();
        priority_queue<tuple<int,int,int>,vector<tuple<int,int,int>>,cmp> Q;
        vector<vector<bool>> visited(N,vector<bool>(N,false));
        Q.push({grid[0][0],0,0});
        visited[0][0]=true;
        int max_h=-1;
        function<bool(int,int)> valid=[&](int i,int j)->bool{
            return i>=0 && i<N && j>=0 && j<N;
        };

        while(!Q.empty()){
            auto [h,i,j]=Q.top();
            Q.pop();
            cout<<"- "<<i<<" "<<j<<endl;
            max_h=max(max_h,h);
            if(i==N-1 && j==N-1) return max_h;

            vector<vector<int>> dirs={{0,-1},{-1,0},{0,1},{1,0}};
            for(auto d:dirs){
                int _i=i+d[0],_j=j+d[1];
                if(valid(_i,_j) && !visited[_i][_j]){
                    Q.push({grid[_i][_j],_i,_j});
                    visited[_i][_j]=true;
                    cout<<" +"<<_i<<" "<<_j<<endl;
                }
            }
        }

        return -1;

    }
};
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