<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) {
        map<int, int> m;
        sort(rectangles.begin(), rectangles.end());
        int bottom = 1e5 + 1, top = -1e5 - 1, left = 1e5 + 1, right = -1e5-1;
        for (auto& r : rectangles) {
            int x1 = r[0], y1 = r[1], x2 = r[2], y2 = r[3];
            bottom = min(bottom, y1);
            top = max(top, y2);
            left = min(left, x1);
            right = max(right, x2);
        }
        m[bottom] = left;
        m[top] = -1e5 - 1;
        for (auto& r : rectangles) {
            int x1 = r[0], y1 = r[1], x2 = r[2], y2 = r[3];
            auto it = m.upper_bound(r[1]);
            auto p = prev(it);
            if (p->second != x1) {                
                return false;
            }
            if (p->first == y1) {
                m.erase(p);
            }
            while (it != m.end() && it->first < y2) {
                if (it->second != x1) {
                    cout << 22 << endl;
                    return false;
                }
                auto temp = it;
                ++it;
                m.erase(temp);
            }
            m[y1] = x2;
            if (!m.contains(y2)) {
                m[y2] = x1;
            }
        }
        return true;
    }
};
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