<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) {
if (rectangles.size() == 0 || rectangles[0].size() == 0) return false;

		int x1 = INT_MAX;
		int x2 = INT_MIN;
		int y1 = INT_MAX;
		int y2 = INT_MIN;

		unordered_set<string> set;
		long area = 0;

		for (auto rect : rectangles) {
			x1 = min(rect[0], x1);
			y1 = min(rect[1], y1);
			x2 = max(rect[2], x2);
			y2 = max(rect[3], y2);

			area += (rect[2] - rect[0]) * long (rect[3] - rect[1]);

			string s1 = to_string(rect[0]) + " " + to_string(rect[1]);
			string s2 = to_string(rect[0]) + " " + to_string(rect[3]);
			string s3 = to_string(rect[2]) + " " + to_string(rect[3]);
			string s4 = to_string(rect[2]) + " " + to_string(rect[1]);

			if (set.find(s1) != set.end())
				set.erase(s1);
			else
				set.insert(s1);
			if (set.find(s2) != set.end())
				set.erase(s2);
			else
	   		       set.insert(s2);
			if (set.find(s3) != set.end())
				set.erase(s3);
			else
				set.insert(s3);
			if (set.find(s4) != set.end())
				set.erase(s4);
			else
				set.insert(s4);


	}
		
if (set.find(to_string(x1) + " " + to_string(y1)) == set.end() || set.find(to_string(x1) + " " + to_string(y2)) == set.end() || set.find(to_string(x2) + " " + to_string(y1)) == set.end() || set.find(to_string(x2) + " " + to_string(y2)) == set.end() || set.size() != 4)
		return false;

	return area == (x2 - x1) * long (y2 - y1);
}
};
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