Using the definitions and procedures of the exercise : “” that you need, your task is to write a program that reads a series of sequences of rectangles, and for each one prints the final result of their intersection.

**Input**

Input consists of several sequence of rectangles.
Each sequence starts with a natural strictly positive *n*,
followed by the description of *n* rectangles (four integer numbers each one).
A special sequence with *n* = 0 indicates the end of the input.

**Output**

For each sequence of rectangles,
print the final result of their intersection
following the format of the instance.
If the intersection is empty (that is, if has area zero),
print “`empty intersection`”.

Public test cases

**Input**

3 0 10 0 10 2 4 2 4 3 5 3 5 2 -10 -5 0 5 -4 -2 2 3 1 1 2 3 4 2 0 1 0 1 1 2 0 1 0

**Output**

bottom left point = (3, 3); top right point = (4, 4) empty intersection bottom left point = (1, 3); top right point = (2, 4) empty intersection

Information

- Author
- Salvador Roura
- Language
- English
- Translator
- Carlos Molina
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++
- User solutions
- C++