code: 
  """simple docstring"""
  import math
  from decimal import Decimal, getcontext
  
  
  
  
  def     __lowerCamelCase  (		UpperCamelCase__ = 400_0000      ):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	try:
  		_UpperCAmelCase =						int(SCREAMING_SNAKE_CASE__      )
  	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."      )
  	_UpperCAmelCase =						100
  	_UpperCAmelCase =						(Decimal(5      ) ** Decimal(0.5      ) + 1) / Decimal(2      )
  
  	_UpperCAmelCase =						(math.floor(math.log(n * (phi + 2)				,     SCREAMING_SNAKE_CASE__      ) - 1      ) // 3) * 3 + 2
  	_UpperCAmelCase =						Decimal(round(phi ** Decimal(index + 1      )      )      ) / (phi + 2)
  	_UpperCAmelCase =						num // 2
  	return int(SCREAMING_SNAKE_CASE__      )
  
  
  if __name__ == "__main__":
  			print(f'''{solution() = }''')
  
  
  
  
  
style_context: 
  """simple docstring"""
  def     __lowerCamelCase  (		UpperCamelCase__      ):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	if not isinstance(UpperCamelCase__				,     UpperCamelCase__      ):
  		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__      ):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	if not isinstance(UpperCamelCase__				,     UpperCamelCase__      ):
  		raise TypeError("dynamic_lucas_number accepts only integer arguments."      )
  	_UpperCAmelCase ,      _UpperCAmelCase =						2, 1
  	for _ in range(UpperCamelCase__      ):
  		_UpperCAmelCase ,      _UpperCAmelCase =						b, a + b
  	return a
  
  
  if __name__ == "__main__":
  			from doctest import testmod
  
  			testmod()
  			__magic_name__		       =				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)))
  
  
  
  
  