<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:
        left = rectangles[0][0]
        right = rectangles[0][2]
        bottom = rectangles[0][1]
        top = rectangles[0][3]
        vertex = {}
        area = 0
        for x, y, a, b in rectangles:
            corners = ((x, y), (x, b), (a, y), (a, b))
            if x < left:
                left = x
            if y < bottom:
                bottom = y
            if a > right:
                right = a
            if b > top:
                top = b
            for corner in corners:
                try:
                    vertex[corner] = not vertex[corner]
                except:
                    vertex[corner] = True
            area += (b-y)*(a-x)
        # print(area)
        if area != (top-bottom)*(right-left):
            return False
        for corner in ((left, top), (left, bottom), (right, top), (right, bottom)):
            try:
                vertex[corner] = not vertex[corner]
            except:
                vertex[corner] = True
        
        # print(vertex)
        for i in vertex:
            if vertex[i]:
                return False
        return True
        """
        if area < 50000000:
            squares = set()
            for rectangle in rectangles:
                for x in range(rectangle[0], rectangle[2]):
                    for y in range(rectangle[1], rectangle[3]):
                        if (x, y) in squares:
                            print((x, y))
                            return False
                        squares.add((x, y))
        else:
            for rect in range(len(rectangles)):
                for rect2 in rectangles[rect+1:]:
                    if rectangles[rect][0] < rect2[2] and rectangles[rect][2] > rect2[0] and  rectangles[rect][1] < rect2[3] and rectangles[rect][3] > rect2[1]:
                        return False
        return True
        """
24900