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class Solution:
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    def isRectangleCover(self, rectangles: List[List[int]]) -> bool:
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        X1, Y1 = float("inf"), float("inf")
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        X2, Y2 = -float("inf"), -float("inf")
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        points = set()
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        actual_area = 0
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        for x1, y1, x2, y2 in rectangles:
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            # calculate the coords of the potential perfect rectangle
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            X1, Y1 = min(X1, x1), min(Y1, y1)
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            X2, Y2 = max(X2, x2), max(Y2, y2)
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            # add up to the actual_area, so we can check against to see if thers is any part overwritten.
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            actual_area += (x2 - x1) * (y2 - y1)
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            # proving steps in https://labuladong.github.io/algo/4/32/131/
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            for p in [(x1, y1), (x1, y2), (x2, y1), (x2, y2)]:
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                if p in points:
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                    points.remove(p)
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                else:
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                    points.add(p)
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        # check the area
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        expected_area = (X2 - X1) * (Y2 - Y1)
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        if actual_area != expected_area:
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            return False
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        if len(points) != 4:
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            return False
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        if (X1, Y1) not in points:
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            return False
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        if (X1, Y2) not in points:
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            return False
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        if (X2, Y1) not in points:
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            return False
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        if (X2, Y2) not in points:
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            return False
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        return True