input: Write a function to implement the `StringComparator` class described in the task, which receives two strings and provides methods for comparing them based on equality, difference, and similarity up to a provided threshold. If the two strings are equal, the method should return True; otherwise, it should return False. Similarly, if the two strings are different, the method should return True; otherwise, it should return False. For the similarity comparison, the method should compute the edit distance and compare it to a threshold, returning True if it is less than the threshold and False otherwise. If the input strings are empty, the methods should return True for both `is_equal` and `is_similar` (with default threshold), and False for `is_different`.
  
  class StringComparator:
  
  def __init__(self, string1, string2):
   self.string1 = string1
   self.string2 = string2
  
  def is_equal(self):
   return self.string1 == self.string2
  
  def is_different(self):
   return self.string1 != self.string2
  
  def is_similar(self, threshold=0.5):
   if self.string1 == '' and self.string2 == '':
   return True
   distance = edit_distance(self.string1, self.string2)
   max_length = max(len(self.string1), len(self.string2))
  
   return distance / max_length < threshold
  
  assert StringComparator("hello", "hello").is_equal() == True
  assert StringComparator("hello", "world").is_equal() == False
  assert StringComparator("hello", "world").is_different() == True
  assert StringComparator("hello", "world").is_similar(threshold=0.5) == False
  assert StringComparator("kitten", "sitting").is_similar(threshold=0.4) == True
  assert StringComparator("", "").is_equal() == True
  assert StringComparator("", "").is_different() == False
  assert StringComparator("", "").is_similar() == True
output: def __init__(self, string1, string2):
   self.string1 = string1
   self.string2 = string2
  
  def is_equal(self):
   return self.string1 == self.string2
  
  def is_different(self):
   return self.string1 != self.string2
  
  def is_similar(self, threshold=0.5):
   if self.string1 == '' and self.string2 == '':
    return True
   distance = edit_distance(self.string1, self.string2)
   max_length = max(len(self.string1), len(self.string2))
   return distance / max_length < threshold