<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):
        # Helper function to calculate area
        def area(rect):
            return (rect[2] - rect[0]) * (rect[3] - rect[1])
        
        # Calculate the total area of all rectangles
        total_area = sum(area(rect) for rect in rectangles)
        
        # Find the bounding rectangle
        min_x = min(rect[0] for rect in rectangles)
        min_y = min(rect[1] for rect in rectangles)
        max_x = max(rect[2] for rect in rectangles)
        max_y = max(rect[3] for rect in rectangles)
        
        bounding_area = (max_x - min_x) * (max_y - min_y)
        
        # If the total area is not equal to the bounding rectangle area, return False
        if total_area != bounding_area:
            return False
        
        # Count the occurrences of each corner point
        from collections import defaultdict
        point_count = defaultdict(int)
        
        for rect in rectangles:
            x1, y1, x2, y2 = rect
            corners = [(x1, y1), (x1, y2), (x2, y1), (x2, y2)]
            for corner in corners:
                point_count[corner] += 1
        
        # Check if the corner points of the bounding rectangle appear exactly once
        # and all other points appear exactly twice or four times
        expected_corners = [(min_x, min_y), (min_x, max_y), (max_x, min_y), (max_x, max_y)]
        for point, count in point_count.items():
            if point in expected_corners:
                if count != 1:
                    return False
            else:
                if count not in [2, 4]:
                    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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