<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:
    def isRectangleCover(self, rectangles: List[List[int]]) -> bool:
        # Define helper function to calculate area
        def area(rectangle):
            x1, y1, x2, y2 = rectangle
            return (x2 - x1) * (y2 - y1)

        # Calculate the area of each smaller rectangle and sum them up
        total_area = sum(area(rect) for rect in rectangles)

        # Find the bounding rectangle (min_x, min_y, max_x, max_y)
        X1, Y1 = min(x for x, y, _, _ in rectangles), min(y for _, y, _, _ in rectangles)
        X2, Y2 = max(x for _, _, x, _ in rectangles), max(y for _, _, _, y in rectangles)

        # Calculate the area of the bounding rectangle
        bounding_area = (X2 - X1) * (Y2 - Y1)

        # If the areas are not equal, return False
        if total_area != bounding_area:
            return False

        # Use a set to keep track of corners
        corners = set()

        # Iterate through each rectangle and update the set of corners
        for x1, y1, x2, y2 in rectangles:
            for point in [(x1, y1), (x1, y2), (x2, y1), (x2, y2)]:
                if point in corners:
                    corners.remove(point)
                else:
                    corners.add(point)

        # Check if only four corners are left and they are the corners of the bounding rectangle
        if len(corners) != 4 or corners != {(X1, Y1), (X1, Y2), (X2, Y1), (X2, Y2)}:
            return False

        return True

# Example usage:
solution = Solution()
rectangles = [[1,1,3,3],[3,1,4,2],[3,2,4,4],[1,3,2,4],[2,3,3,4]]
print(solution.isRectangleCover(rectangles))  # Output: True
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