<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:
    #define ll long long int
    bool isRectangleCover(vector<vector<int>>& rec) {
        ll n=rec.size();
        if(n==1) return 1;
        sort(rec.begin(),rec.end());
        map<pair<ll,ll>,ll>mp;
        ll mnx=INT_MAX, mxx=INT_MIN, mny=INT_MAX, mxy=INT_MIN;
        ll area=0;
        for(auto pr: rec){
            ll x1=pr[0], y1=pr[1], x2=pr[2], y2=pr[3];
            mnx=min(mnx,x1);  mxx=max(mxx,x2);
            mny=min(mny,y1);  mxy=max(mxy,y2);
            area += (x2-x1)*(y2-y1);
            mp[{x1,y1}]++;  mp[{x2,y1}]++;
            mp[{x1,y2}]++;  mp[{x2,y2}]++;
        }
        ll sz=0, f=0;
        for(auto pr: mp){
            if(pr.second==1) sz++; 
            else if(pr.second&1) {f=1;}
            // cout<<pr.second<<" ";
        }

        ll narea= (mxx-mnx)*(mxy-mny);
        // cout<<narea<<" "<<area<<endl;
        if(f==1 or sz!=4 or mp[{mnx,mny}]!=1 or mp[{mnx,mxy}]!=1 
        or mp[{mxx,mny}]!=1 or mp[{mxx,mxy}]!=1) return 0;
        if(sz==4 and narea==area) return 1;
        return 0;
    }
};
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