<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) {
        vector<vector<int>>x,y;
        long long tot = 0;
        for(auto r : rectangles){
            x.push_back({r[0],r[2],r[1],r[3]});
            y.push_back({r[1],r[3],r[0],r[2]});
            tot+=(long long)(r[2]-r[0]) *(long long) (r[3]-r[1]);
        }
        sort(x.begin(),x.end());
        sort(y.begin(),y.end());
        //for(auto k : x) cout << "(" << k[0] << " " << k[1] << "),";
        //cout << endl;
        // for(auto k : y) cout << "(" << k[0] << " " << k[1] << "),";
        //cout << endl;
        int l = x[0][0] , r = x.back()[1], d = y[0][0], u = y.back()[1], endx = x[0][1],endy =y[0][1];
        for(int i = 1; i < x.size(); i++){
            if(endx>x[i][0]) {
                vector<int>a = {x[i-1][2], x[i-1][3]};
                vector<int>b = {x[i][2], x[i][3]};
                if(a[0] > b[0]) swap(a,b);
                if(a[1] > b[0]) return false;
            }
            endx = max(x[i][1],endx);
        }
        for(int i = 1; i < y.size(); i++){
            
            if(endy>y[i][0]) {
                if(y[i-1][3] > y[i][2] || y[i][3] > y[i-1][2]) {
                    vector<int>a = {y[i-1][2], y[i-1][3]};
                    vector<int>b = {y[i][2], y[i][3]};
                    if(a[0] > b[0]) swap(a,b);
                    if(a[1] > b[0]) return false;
                }
            }
            endy = max(y[i][1],endy);
        }
        
        long long area = (long long)(r-l)*(u-d);
        //cout << area <<  " " << tot << endl;
        return tot == area;
    }
};
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