<p>Given an array <code>rectangles</code> where <code>rectangles[i] = [x<sub>i</sub>, y<sub>i</sub>, a<sub>i</sub>, b<sub>i</sub>]</code> represents an axis-aligned rectangle. The bottom-left point of the rectangle is <code>(x<sub>i</sub>, y<sub>i</sub>)</code> and the top-right point of it is <code>(a<sub>i</sub>, b<sub>i</sub>)</code>.</p>

<p>Return <code>true</code> <em>if all the rectangles together form an exact cover of a rectangular region</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/27/perectrec1-plane.jpg" style="width: 300px; height: 294px;" />
<pre>
<strong>Input:</strong> rectangles = [[1,1,3,3],[3,1,4,2],[3,2,4,4],[1,3,2,4],[2,3,3,4]]
<strong>Output:</strong> true
<strong>Explanation:</strong> All 5 rectangles together form an exact cover of a rectangular region.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/27/perfectrec2-plane.jpg" style="width: 300px; height: 294px;" />
<pre>
<strong>Input:</strong> rectangles = [[1,1,2,3],[1,3,2,4],[3,1,4,2],[3,2,4,4]]
<strong>Output:</strong> false
<strong>Explanation:</strong> Because there is a gap between the two rectangular regions.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/27/perfecrrec4-plane.jpg" style="width: 300px; height: 294px;" />
<pre>
<strong>Input:</strong> rectangles = [[1,1,3,3],[3,1,4,2],[1,3,2,4],[2,2,4,4]]
<strong>Output:</strong> false
<strong>Explanation:</strong> Because two of the rectangles overlap with each other.
</pre>

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

<ul>
	<li><code>1 &lt;= rectangles.length &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>rectangles[i].length == 4</code></li>
	<li><code>-10<sup>5</sup> &lt;= x<sub>i</sub> &lt; a<sub>i</sub> &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>5</sup> &lt;= y<sub>i</sub> &lt; b<sub>i</sub> &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution {
public:
    bool isRectangleCover(vector<vector<int>>& rectangles) {
        long long int area=0;
        long long int minX=1e9,minY=1e9;
        long long int maxX=-1e9,maxY=-1e9;
        map<pair<long long int,long long int>,long long int>h;
    
        for(long long int i=0;i<rectangles.size();i++){
            long long int x1=rectangles[i][0];
            long long int y1=rectangles[i][1];
            long long int x2=rectangles[i][2];
            long long int y2=rectangles[i][3];
            minX=min(minX,min(x1,x2));
            minY=min(minY,min(y1,y2));
            maxX=max(maxX,max(x1,x2));
            maxY=max(maxY,max(y1,y2));

            area+=(x2-x1)*(y2-y1);
            h[{x1,y1}]++;
            h[{x2,y2}]++;
            h[{x1,y2}]++;
            h[{x2,y1}]++;
        }
        long long int cnt=0;
        for(auto it: h){
            if(it.second%2==1 && (it.first.first==maxX || it.first.first==minX) && (it.first.second==minY || it.first.second==maxY))cnt++;
            if(it.second%2==1 && !((it.first.first==maxX || it.first.first==minX) && (it.first.second==minY || it.first.second==maxY)))return false;
        }
         cout<<cnt<<endl;
        if(cnt==4 && area==(maxX-minX)*(maxY-minY))return true;
        return false;
    }
};
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