import matplotlib.pyplot as plt

class Interval:
"""
A class that implements interval analysis. The class is initialized with two
real numbers that represent the left and the right endpoints:
parameters:
left endpoint: real number
right endpoint: real number
"""

def __init__(self, left_endpoint, right_endpoint=None):
   """
   initialize the class with two real numbers
   if only one real number is provided, set the right endpoint equals to the left endpoint
   """
   if right_endpoint is None:
         self.left = left_endpoint
         self.right = left_endpoint
   else:
         self.left = left_endpoint
         self.right = right_endpoint

def __add__(self, other_interval):
   """
   method that implements the addition of two intervals
   if the second (right) object is not an Interval instance but a real number
   we define an addition of an Interval instance and a real number
   """
   if not isinstance(other_interval, Interval):
         left = self.left + other_interval
         right = self.right + other_interval
   else:
         left = self.left + other_interval.left
         right = self.right + other_interval.right
   return Interval(left, right)

def __sub__(self, other_interval):
   """
   method that implements subtraction of two intervals
   """
   if not isinstance(other_interval, Interval):
         left = self.left - other_interval
         right = self.right - other_interval
   else:
         left = self.left - other_interval.right
         right = self.right - other_interval.left
   return Interval(left, right)

def __mul__(self, other_interval):
   """
   method that implements multiplication of two intervals
   """
   if not isinstance(other_interval, Interval):
         L = [self.left*other_interval, self.right*other_interval]
   else:
         L = [
            self.left*other_interval.left,
            self.left*other_interval.right,
            self.right*other_interval.left,
            self.right*other_interval.right
         ]
   left = min(L)
   right = max(L)
   return Interval(left, right)

def __truediv__(self, other_interval):
   """
   method that implements divison of two intervals
   """
   try:
         L = [
            self.left/other_interval.left,
            self.left/other_interval.right,
            self.right/other_interval.left,
            self.right/other_interval.right]
   except ZeroDivisionError

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