


'''simple docstring'''
def 				lowerCamelCase_   (   __UpperCamelCase				:					int		)				->  int:







     """simple docstring"""
     if not isinstance(__snake_case       ,						__snake_case		):
          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 				lowerCamelCase_   (   __UpperCamelCase				:					Union[str, Any]		)				->  int:







     """simple docstring"""
     if not isinstance(__snake_case       ,						__snake_case		):
          raise TypeError('dynamic_lucas_number accepts only integer arguments.'		)
     _A		,							_A				=       2, 1
     for _ in range(__snake_case		):
          _A		,							_A				=       b, a + b
     return a


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

    testmod()
    lowerCAmelCase  =				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)))





'''simple docstring'''
from __future__ import annotations

def 				lowerCamelCase_   (   __UpperCamelCase				:					list[int | float]		)				->  int | float:







     """simple docstring"""
     if len(__UpperCamelCase		) == 0:
          raise ValueError('find_max() arg is an empty sequence'		)
     _A				=       nums[0]
     for x in nums:
          if x > max_num:
               _A				=       x
     return max_num


if __name__ == "__main__":
    import doctest

    doctest.testmod(verbose=True)





