


"""simple docstring"""





import math
from decimal import Decimal, getcontext





def     lowercase__	(  lowerCamelCase     :  int = 4_0_0_0_0_0_0				)					->     int:

  try:
    lowerCAmelCase__    :    Tuple								=					int(lowerCamelCase				)
  except (TypeError, ValueError):
    raise TypeError("Parameter n must be int or castable to int."				)
  if n <= 0:
    raise ValueError("Parameter n must be greater than or equal to one."				)
  lowerCAmelCase__    :    Optional[int]								=					1_0_0
  lowerCAmelCase__    :    Tuple								=					(Decimal(5				) ** Decimal(0.5				) + 1) / Decimal(2				)

  lowerCAmelCase__    :    Optional[Any]								=					(math.floor(math.log(n * (phi + 2)				,	lowerCamelCase				) - 1				) // 3) * 3 + 2
  lowerCAmelCase__    :    Any								=					Decimal(round(phi ** Decimal(index + 1				)				)				) / (phi + 2)
  lowerCAmelCase__    :    List[str]								=					num // 2
  return int(lowerCamelCase				)


if __name__ == "__main__":
   print(f"""{solution() = }""")




"""simple docstring"""





def     lowercase__	(  lowerCamelCase     :  int				)					->     int:
  if not isinstance(lowerCamelCase				,	lowerCamelCase				):
    raise TypeError("recursive_lucas_number accepts only integer arguments."				)
  if n_th_number == 0:
    return 2
  if n_th_number == 1:
    return 1

  return recursive_lucas_number(n_th_number - 1				) + recursive_lucas_number(
      n_th_number - 2				)





def     lowercase__	(  lowerCamelCase     :  int				)					->     int:
  if not isinstance(lowerCamelCase				,	lowerCamelCase				):
    raise TypeError("dynamic_lucas_number accepts only integer arguments."				)
  lowerCAmelCase__				,		lowerCAmelCase__    :    str								=					2, 1
  for _ in range(lowerCamelCase				):
    lowerCAmelCase__				,		lowerCAmelCase__    :    str								=					b, a + b
  return a


if __name__ == "__main__":
   from doctest import testmod

   testmod()
   __UpperCAmelCase    				=      int(input("Enter the number of terms in lucas series:\n").strip())
   print("Using recursive function to calculate lucas series:")
   print(" ".join(str(recursive_lucas_number(i)) for i in range(n)))
   print("\nUsing dynamic function to calculate lucas series:")
   print(" ".join(str(dynamic_lucas_number(i)) for i in range(n)))
