


"""simple docstring"""





__UpperCAmelCase    				=      (1, 153, 370, 371, 1_634, 24_678_051, 115_132_219_018_763_992_565_095_597_973_971_522_401)
__UpperCAmelCase    				=      (-153, -1, 0, 1.2, 200, "A", [], {}, None)





def     lowercase__	(  lowerCamelCase     :  int				)					->     bool:
  if not isinstance(lowerCamelCase				,	lowerCamelCase				) or n < 1:
    return False

  # Initialization of sum and number of digits.
  lowerCAmelCase__    :    List[str]								=					0
  lowerCAmelCase__    :    Any								=					0
  lowerCAmelCase__    :    int								=					n
  # Calculation of digits of the number
  while temp > 0:
    number_of_digits += 1
    temp //= 1_0
  # Dividing number into separate digits and find Armstrong number
  lowerCAmelCase__    :    Union[str, Any]								=					n
  while temp > 0:
    lowerCAmelCase__    :    int								=					temp % 1_0
    total += rem**number_of_digits
    temp //= 1_0
  return n == total





def     lowercase__	(  lowerCamelCase     :  int				)					->     bool:
  if not isinstance(lowerCamelCase				,	lowerCamelCase				) or n < 1:
    return False

  # Init a "histogram" of the digits
  lowerCAmelCase__    :    Tuple								=					[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
  lowerCAmelCase__    :    str								=					0
  lowerCAmelCase__    :    Optional[Any]								=					0
  lowerCAmelCase__    :    Dict								=					n
  while temp > 0:
    lowerCAmelCase__				,		lowerCAmelCase__    :    List[str]								=					divmod(lowerCamelCase				,	1_0				)
    digit_histogram[rem] += 1
    digit_total += 1

  for cnt, i in zip(lowerCamelCase				,	range(len(lowerCamelCase				)				)				):
    total += cnt * i**digit_total

  return n == total





def     lowercase__	(  lowerCamelCase     :  int				)					->     bool:
  if not isinstance(lowerCamelCase				,	lowerCamelCase				) or n < 1:
    return False
  lowerCAmelCase__    :    int								=					len(str(lowerCamelCase				)				)  # the power that all digits will be raised to
  # check if sum of each digit multiplied expo times is equal to number
  return n == sum(int(lowerCamelCase				) ** expo for i in str(lowerCamelCase				)				)





def     lowercase__	(  )					->     int:
  lowerCAmelCase__    :    Any								=					int(input("Enter an integer to see if it is an Armstrong number: "				).strip()				)
  print(F"{num} is {'' if armstrong_number(lowerCamelCase				) else 'not '}an Armstrong number."				)
  print(F"{num} is {'' if narcissistic_number(lowerCamelCase				) else 'not '}an Armstrong number."				)
  print(F"{num} is {'' if pluperfect_number(lowerCamelCase				) else 'not '}an Armstrong number."				)


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   main()




"""simple docstring"""





from __future__ import annotations

__UpperCAmelCase    				=      [2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]

class  lowercase_  :







      def __init__(      self :							int		,  _lowercase :							int    ):
        lowerCAmelCase__    :    int								=					-1
        lowerCAmelCase__    :    int								=					-1
        lowerCAmelCase__    :    list[int]								=					[-1] * length
        lowerCAmelCase__    :    Node | None								=					None
        lowerCAmelCase__    :    Node | None								=					None







      def __repr__(      self :							List[Any]    ):
        return f"Node(min_value={self.minn} max_value={self.maxx})"





def     lowercase__	(  lowerCamelCase     :  list[int]				)					->     Node | None:
  lowerCAmelCase__    :    Any								=					Node(len(lowerCamelCase				)				)
  lowerCAmelCase__				,		lowerCAmelCase__    :    Any								=					min(lowerCamelCase				), max(lowerCamelCase				)
  # Leaf node case where the node contains only one unique value
  if root.minn == root.maxx:
    return root
  lowerCAmelCase__    :    str								=					(root.minn + root.maxx) // 2

  lowerCAmelCase__    :    list[int]								=					[]
  lowerCAmelCase__    :    list[int]								=					[]

  for index, num in enumerate(lowerCamelCase				):
    if num <= pivot:
      left_arr.append(lowerCamelCase				)
    else:
      right_arr.append(lowerCamelCase				)
    lowerCAmelCase__    :    Optional[Any]								=					len(lowerCamelCase				)
  lowerCAmelCase__    :    List[str]								=					build_tree(lowerCamelCase				)
  lowerCAmelCase__    :    List[Any]								=					build_tree(lowerCamelCase				)
  return root





def     lowercase__	(  lowerCamelCase     :  Node | None				,	lowerCamelCase     :  int				,	lowerCamelCase     :  int				)					->     int:
  if index < 0 or node is None:
    return 0
  # Leaf node cases
  if node.minn == node.maxx:
    return index + 1 if node.minn == num else 0
  lowerCAmelCase__    :    int								=					(node.minn + node.maxx) // 2
  if num <= pivot:
    # go the left subtree and map index to the left subtree
    return rank_till_index(node.left				,	lowerCamelCase				,	node.map_left[index] - 1				)
  else:
    # go to the right subtree and map index to the right subtree
    return rank_till_index(node.right				,	lowerCamelCase				,	index - node.map_left[index]				)





def     lowercase__	(  lowerCamelCase     :  Node | None				,	lowerCamelCase     :  int				,	lowerCamelCase     :  int				,	lowerCamelCase     :  int				)					->     int:
  if start > end:
    return 0
  lowerCAmelCase__    :    int								=					rank_till_index(lowerCamelCase				,	lowerCamelCase				,	lowerCamelCase				)
  lowerCAmelCase__    :    Optional[Any]								=					rank_till_index(lowerCamelCase				,	lowerCamelCase				,	start - 1				)
  return rank_till_end - rank_before_start





def     lowercase__	(  lowerCamelCase     :  Node | None				,	lowerCamelCase     :  int				,	lowerCamelCase     :  int				,	lowerCamelCase     :  int				)					->     int:
  if index > (end - start) or start > end or node is None:
    return -1
  # Leaf node case
  if node.minn == node.maxx:
    return node.minn
  # Number of elements in the left subtree in interval [start, end]
  lowerCAmelCase__    :    List[str]								=					node.map_left[end] - (
      node.map_left[start - 1] if start else 0
  )
  if num_elements_in_left_tree > index:
    return quantile(
        node.left				,	lowerCamelCase				,	(node.map_left[start - 1] if start else 0)				,	node.map_left[end] - 1				,	)
  else:
    return quantile(
        node.right				,	index - num_elements_in_left_tree				,	start - (node.map_left[start - 1] if start else 0)				,	end - node.map_left[end]				,	)





def     lowercase__	(  lowerCamelCase     :  Node | None				,	lowerCamelCase     :  int				,	lowerCamelCase     :  int				,	lowerCamelCase     :  int				,	lowerCamelCase     :  int				)					->     int:
  if (
      start > end
      or node is None
      or start_num > end_num
      or node.minn > end_num
      or node.maxx < start_num
  ):
    return 0
  if start_num <= node.minn and node.maxx <= end_num:
    return end - start + 1
  lowerCAmelCase__    :    List[str]								=					range_counting(
      node.left				,	(node.map_left[start - 1] if start else 0)				,	node.map_left[end] - 1				,	lowerCamelCase				,	lowerCamelCase				,	)
  lowerCAmelCase__    :    List[str]								=					range_counting(
      node.right				,	start - (node.map_left[start - 1] if start else 0)				,	end - node.map_left[end]				,	lowerCamelCase				,	lowerCamelCase				,	)
  return left + right


if __name__ == "__main__":
   import doctest

   doctest.testmod()
