





'''simple docstring'''


def    __a (     UpperCAmelCase       ,			UpperCAmelCase    )      ->int:



	"""simple docstring"""







	if not root or root not in binary_tree_mirror_dictionary:
		return
	A  ,    A							  =      binary_tree_mirror_dictionary[root][:2]
	A							  =      [right_child, left_child]
	binary_tree_mirror_dict(UpperCAmelCase       ,			UpperCAmelCase    )
	binary_tree_mirror_dict(UpperCAmelCase       ,			UpperCAmelCase    )




def    __a (     UpperCAmelCase       ,			UpperCAmelCase = 1    )      ->dict:



	"""simple docstring"""







	if not binary_tree:
		raise ValueError("""binary tree cannot be empty"""    )
	if root not in binary_tree:
		A							  =      f"""root {root} is not present in the binary_tree"""
		raise ValueError(UpperCAmelCase    )
	A							  =      dict(UpperCAmelCase    )
	binary_tree_mirror_dict(UpperCAmelCase       ,			UpperCAmelCase    )
	return binary_tree_mirror_dictionary


if __name__ == "__main__":
				_lowerCamelCase				:	Dict				    =       {1: [2, 3], 2: [4, 5], 3: [6, 7], 7: [8, 9]}
				print(f"Binary tree: {binary_tree}")
				_lowerCamelCase				:	Any				    =       binary_tree_mirror(binary_tree, 5)
				print(f"Binary tree mirror: {binary_tree_mirror_dictionary}")








'''simple docstring'''


class 							__UpperCAmelCase  :







		'''simple docstring'''







		def __init__(self						:      List[str]      ):
			# numbermap keys are the number and its values are lists of indexes sorted
			# in ascending order
			A							  =      {}
			# indexmap keys are an index and it's values are the number at that index
			A							  =      {}







		def        A     (self						:      Union[str, Any]      ,      _lowerCAmelCase						:      list | str | range      ,      _lowerCAmelCase						:      int      ):
			if isinstance(_lowerCAmelCase      ,      (range, str)      ):
				A							  =      list(_lowerCAmelCase      )
			elif not isinstance(_lowerCAmelCase      ,      _lowerCAmelCase      ):
				raise TypeError(
				    """binary_search_delete() only accepts either a list, range or str"""      )

			A							  =      0
			A							  =      len(_lowerCAmelCase      ) - 1

			while low <= high:
				A							  =      (low + high) // 2
				if array[mid] == item:
					array.pop(_lowerCAmelCase      )
					return array
				elif array[mid] < item:
					A							  =      mid + 1
				else:
					A							  =      mid - 1
			raise ValueError(
			    """Either the item is not in the array or the array was unsorted"""      )







		def        A     (self						:      Dict      ,      _lowerCAmelCase						:      list | str | range      ,      _lowerCAmelCase						:      int      ):
			if isinstance(_lowerCAmelCase      ,      (range, str)      ):
				A							  =      list(_lowerCAmelCase      )
			elif not isinstance(_lowerCAmelCase      ,      _lowerCAmelCase      ):
				raise TypeError(
				    """binary_search_insert() only accepts either a list, range or str"""      )

			A							  =      0
			A							  =      len(_lowerCAmelCase      ) - 1

			while low <= high:
				A							  =      (low + high) // 2
				if array[mid] == index:
					# If the item already exists in the array,
					# insert it after the existing item
					array.insert(mid + 1      ,      _lowerCAmelCase      )
					return array
				elif array[mid] < index:
					A							  =      mid + 1
				else:
					A							  =      mid - 1

        # If the item doesn't exist in the array, insert it at the appropriate position
			array.insert(_lowerCAmelCase      ,      _lowerCAmelCase      )
			return array







		def        A     (self						:      List[str]      ,      _lowerCAmelCase						:      int      ,      _lowerCAmelCase						:      int      ):
			# Remove previous index
			if index in self.indexmap:
				A							  =      self.indexmap[index]
				if len(self.numbermap[n]      ) == 1:
					del self.numbermap[n]
				else:
					A							  =      self.binary_search_delete(self.numbermap[n]      ,      _lowerCAmelCase      )

        # Set new index
			A							  =      number

			# Number not seen before or empty so insert number value
			if number not in self.numbermap:
				A							  =      [index]

			# Here we need to perform a binary search insertion in order to insert
			# The item in the correct place
			else:
				A							  =      self.binary_search_insert(
				    self.numbermap[number]      ,      _lowerCAmelCase      )







		def        A     (self						:      int      ,      _lowerCAmelCase						:      int      ):
			return self.numbermap.get(_lowerCAmelCase      ,      [-1]      )[0]


if __name__ == "__main__":
				import doctest

				doctest.testmod()

