<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<int,int>> corners;
        int x1 = INT_MAX, y1 = INT_MAX;
        int x2 = INT_MIN, y2 = INT_MIN;
        long area = 0;
        for (const auto& rect: rectangles) {
            x1 = min(x1, rect[0]);
            y1 = min(y1, rect[1]);
            x2 = max(x2, rect[2]);
            y2 = max(y2, rect[3]);

            area += ((long) rect[2] - rect[0]) * ((long) rect[3] - rect[1]);
            vector<pair<int, int>> curCorners = {{rect[0], rect[1]}, {rect[0], rect[3]}, {rect[2], rect[1]}, {rect[2], rect[3]}};

            for (auto& corner: curCorners) {
                if (corners.find(corner) != corners.end()) {
                    corners.erase(corner);
                } else {
                    corners.insert(corner);
                }
            }
        }

        if (area != ((long) x2 - x1) * ((long) y2 - y1)) {
            return false;
        }
        if (corners.size() != 4) {
            return false;
        }

        vector<pair<int, int>> curCorners = {{x1, y1}, {x1, y2}, {x2, y1}, {x2, y2}};

        for (auto& corner: curCorners) {
            if (corners.find(corner) == corners.end()) {
                return false;
            } 
        }
        return true;
    }
};
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