Define a class Point that can be used to represent points in the two-dimensional Euclidean plane. Two arguments must be passed when creating a new point \((x, y)\) (Point): i) the \(x\)-coordinate (int) of the point and ii) the \(y\)-coordinate (int) of the point.

Define a class Rectangle that can be used to represent rectangles in the two-dimensional Euclidean plane. Three arguments must be passed when creating a new rectangle (Rectangle): i) the point \(p\) (Point) in the top left corner of the rectangle, ii) the width \(w\) (int) of the rectangle and iii) the height \(h\) (int) of the rectangle. If it does not hold that \(b,h > 0\), an AssertionError must be raised with the message invalid rectangle. Rectangles (Rectangle) must at least support the following methods:

• A method surface_area that returns the surface area (int, \(b \times h\)) of the rectangle.

• A method circumference that returns the circumference (int, \(2(b + h)\)) of the rectangle.

• A method bottom_right that returns the point (Punt) in the bottom right corner of the rectangle.

• A method overlap that takes a rectangle (Rectangle). If both rectangles (the rectangle on which the method was called and the rectangle passed as an argument to the method) overlap, the method must return a rectangle (Rectangle) that represents the overlapping region of the two rectangles. Otherwise, the value None must be returned.

If a point (Point) or a rectangle (Rectangle) is passed to the builtin functions repr or str, a string representation (str) of the point or the rectangle must be returned that reads as a Python expression that creates a point or a rectangle at the same location.

Use the convention that the y-axis is pointed downward, that is: Point(1, 1) is above Point(1, 2).

Example

>>> p = Point(3, 4)
>>> p
Point(3, 4)
>>> print(p)
Point(3, 4)

>>> r1 = Rectangle(Point(1, 1), 8, 5)
>>> r2 = Rectangle(Point(2, 3), 9, 2)
>>> r1
Rectangle(Point(1, 1), 8, 5)
>>> print(r2)
Rectangle(Point(2, 3), 9, 2)
>>> r1.surface_area()
40
>>> r1.circumference()
26
>>> r1.bottom_right()
Point(9, 6)
>>> r1.overlap(r2)
Rectangle(Point(2, 3), 7, 2)
>>> r2.overlap(Rectangle(Point(0, 0), 2, 2))

>>> Rectangle(Point(3, 4), -2, 7)
Traceback (most recent call last):
AssertionError: invalid rectangle