


"""simple docstring"""





from __future__ import annotations

import math
from itertools import permutations





def     lowercase__	(  lowerCamelCase     :  Optional[int]				)					->     List[str]:


  if 1 < number < 4:
    # 2 and 3 are primes
    return True
  elif number < 2 or number % 2 == 0 or number % 3 == 0:
    # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
    return False

  # All primes number are in format of 6k +/- 1
  for i in range(5				,	int(math.sqrt(_A				) + 1				)				,	6				):
    if number % i == 0 or number % (i + 2) == 0:
      return False
  return True





def     lowercase__	(  lowerCamelCase     :  Optional[Any] = 7				)					->     List[Any]:
  lowerCAmelCase__    :    List[str]								=					"".join(str(_A				) for i in range(1				,	n + 1				)				)
  lowerCAmelCase__    :    int								=					[int("".join(_A				)				) for i in permutations(_A				,	_A				)]
  lowerCAmelCase__    :    Union[str, Any]								=					[num for num in perm_list if is_prime(_A				)]
  return max(_A				) if pandigitals else 0


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)))
