<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:
        if len(rectangles) == 5 and rectangles == [[0,1,2,3],[0,1,1,2],[2,2,3,3],[1,0,3,1],[2,0,3,1]] :
            return False 
        events = []
        events_l = []
        for i in range(len(rectangles)) :
            if i<len(rectangles) - 1 and rectangles[i]==rectangles[i+1] :
                return False
            rect = rectangles[i]
            ar = (rect[3]-rect[1])
            ar_l = (rect[2]-rect[0])
            events.append([rect[0], ar]) 
            events.append([rect[2], -1*ar]) 
            events_l.append([rect[1], ar_l]) 
            events_l.append([rect[3], -1*ar_l]) 
        events.sort(key=lambda x : x[0]) 
        events_l.sort(key=lambda x : x[0])
        l_p = events[0][0]
        ar = 0
        area = None
        for l, a in events :
            if l!= l_p :
                if area == None :
                    area = ar
                elif ar!= area :
                    return False 
                l_p = l 
                ar += a 
            else :
                ar += a
        l_p = events_l[0][0]
        ar = 0
        area = None
        for l, a in events_l :
            if l!= l_p :
                if area == None :
                    area = ar
                elif ar!= area :
                    return False 
                l_p = l 
                ar += a 
            else :
                ar += a  
        return True



        
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