<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) {
        set<pair<long long, long long>> corners;
        int minx = INT_MAX;
        int miny = INT_MAX;
        int maxx = INT_MIN;
        int maxy = INT_MIN;
        long long area = 0;

        for(const auto& rect : rectangles){
            minx = min(minx, rect[0]);
            miny = min(miny, rect[1]);
            maxx = max(maxx, rect[2]);
            maxy = max(maxy, rect[3]);
            area += static_cast<long long>(rect[2]- rect[0]) * (rect[3] - rect[1]);
            pair<long long, long long> p1 = {rect[0], rect[1]};
            pair<long long, long long> p2 = {rect[0], rect[3]};
            pair<long long, long long> p3 = {rect[2], rect[3]};
            pair<long long, long long> p4 = {rect[2], rect[1]};

        

        if(!corners.insert(p1).second) corners.erase(p1);
        if(!corners.insert(p2).second) corners.erase(p2);
        if(!corners.insert(p3).second) corners.erase(p3);
        if(!corners.insert(p4).second) corners.erase(p4);
    }

    if(corners.size() != 4 ||
       corners.count({minx, miny}) == 0 ||
       corners.count({minx, maxy}) == 0 ||
       corners.count({maxx, miny}) == 0 ||
       corners.count({maxx, maxy}) == 0) {
       return false;

    }

    long long exceptedArea = static_cast<long long>(maxx-minx) * (maxy - miny);
    return area == exceptedArea;
}   
};
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