Rectangle overlap X54942

Statement

html

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.

Public test cases

Input

50 100 0 0      50 100 25 50
50 100 25 50    50 100 0 0
50 100 0 0      50 100 75 50
50 100 75 50    50 100 0 0
50 100 0 0      25 50 0 0
25 50 0 0       50 100 0 0

Output

True
True
False
False
True
True

Information

Author: Gabriel Valiente
Language: English
Official solutions: Python
User solutions: C++ Python