Rectangle in rectangle X58214

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_in_rectangle(r1, r2)

that returns @True@ if all of the corners of a rectangle @r1@ fall inside a rectangle @r2@, and @False@ otherwise. For example, a rectangle of width $50$, height $100$, and lower-left corner $(25, 25)$ falls inside a rectangle of width $100$, height $200$, and lower-left corner $(0, 0)$, but a rectangle of width $50$, height $100$, and lower-left corner $(0, 0)$ does 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 the first rectangle fall inside the second rectangle.