Rectangle overlap X54942

Using the definitions

class Point:
    """attributes: x, y"""

class Rectangle:
    """attributes: width, height, corner"""

and the function @point_in_rectangle@ from problem X53379 (Point in rectangle), write a function

rectangle_overlap(r1, r2)

that returns @True@ if a corner of a rectangle @r1@ falls inside or on the boundary of a rectangle @r2@ but the opposite corner of @r1@ falls outside @r2@ or, conversely, if a corner of @r2@ falls inside or on the boundary of @r1@ but the opposite corner of @r2@ falls outside @r1@, and @False@ otherwise. For example, a rectangle of width $50$, height $100$, and lower-left corner $(0, 0)$ and a rectangle of width $50$, height $100$, and lower-left corner $(25, 50)$ overlap, but a rectangle of width $50$, height $100$, and lower-left corner $(0, 0)$ and a rectangle of width $50$, height $100$, and lower-left corner $(75, 50)$ do not.

Input

The input consists of several pairs of rectangles (four non-negative integer numbers for each: the width, the height, and the coordinates of the lower-left corner).

Output

For each pair of rectangles, print whether or not they overlap.