




"""simple docstring"""







def 							lowercase    (snake_case__      :       int       )   ->     int:


				'''simple docstring'''






				lowerCAmelCase              = 0
				while num > 0:
								digit_sum += num % 10
								num //= 10
				return digit_sum





def 							lowercase    (snake_case__      :       int = 100       )   ->     int:


				'''simple docstring'''






				lowerCAmelCase              = 1
				lowerCAmelCase              = 2

				for i in range(2					,				max_n + 1       ):
								lowerCAmelCase              = pre_numerator
								lowerCAmelCase              = 2 * i // 3 if i % 3 == 0 else 1
								lowerCAmelCase              = cur_numerator
								lowerCAmelCase              = e_cont * pre_numerator + temp

				return sum_digits(lowerCAmelCase__       )


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










"""simple docstring"""







from ..utils import DummyObject, requires_backends







class       UpperCamelCase__   (	metaclass=lowercase_  ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE  				=     ["""flax"""]



      def __init__(      self				:      List[Any]    ,			*SCREAMING_SNAKE_CASE_				:      Optional[int]    ,			**SCREAMING_SNAKE_CASE_				:      Any       ):
        requires_backends(self    ,			['flax']       )



      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Any    ,			*SCREAMING_SNAKE_CASE_				:      int    ,			**SCREAMING_SNAKE_CASE_				:      List[str]       ):
        requires_backends(cls    ,			['flax']       )





      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      int    ,			*SCREAMING_SNAKE_CASE_				:      Optional[int]    ,			**SCREAMING_SNAKE_CASE_				:      Optional[int]       ):
        requires_backends(cls    ,			['flax']       )







class       UpperCamelCase__   (	metaclass=lowercase_  ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE  				=     ["""flax"""]



      def __init__(      self				:      Tuple    ,			*SCREAMING_SNAKE_CASE_				:      Tuple    ,			**SCREAMING_SNAKE_CASE_				:      Any       ):
        requires_backends(self    ,			['flax']       )



      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Union[str, Any]    ,			*SCREAMING_SNAKE_CASE_				:      Dict    ,			**SCREAMING_SNAKE_CASE_				:      Dict       ):
        requires_backends(cls    ,			['flax']       )





      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Dict    ,			*SCREAMING_SNAKE_CASE_				:      List[str]    ,			**SCREAMING_SNAKE_CASE_				:      Optional[Any]       ):
        requires_backends(cls    ,			['flax']       )







class       UpperCamelCase__   (	metaclass=lowercase_  ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE  				=     ["""flax"""]



      def __init__(      self				:      int    ,			*SCREAMING_SNAKE_CASE_				:      Optional[int]    ,			**SCREAMING_SNAKE_CASE_				:      List[str]       ):
        requires_backends(self    ,			['flax']       )



      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      List[Any]    ,			*SCREAMING_SNAKE_CASE_				:      Any    ,			**SCREAMING_SNAKE_CASE_				:      List[Any]       ):
        requires_backends(cls    ,			['flax']       )





      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Union[str, Any]    ,			*SCREAMING_SNAKE_CASE_				:      List[str]    ,			**SCREAMING_SNAKE_CASE_				:      List[str]       ):
        requires_backends(cls    ,			['flax']       )







class       UpperCamelCase__   (	metaclass=lowercase_  ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE  				=     ["""flax"""]



      def __init__(      self				:      Tuple    ,			*SCREAMING_SNAKE_CASE_				:      List[str]    ,			**SCREAMING_SNAKE_CASE_				:      int       ):
        requires_backends(self    ,			['flax']       )



      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Tuple    ,			*SCREAMING_SNAKE_CASE_				:      List[str]    ,			**SCREAMING_SNAKE_CASE_				:      str       ):
        requires_backends(cls    ,			['flax']       )





      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      List[Any]    ,			*SCREAMING_SNAKE_CASE_				:      Dict    ,			**SCREAMING_SNAKE_CASE_				:      int       ):
        requires_backends(cls    ,			['flax']       )







class       UpperCamelCase__   (	metaclass=lowercase_  ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE  				=     ["""flax"""]



      def __init__(      self				:      List[str]    ,			*SCREAMING_SNAKE_CASE_				:      int    ,			**SCREAMING_SNAKE_CASE_				:      int       ):
        requires_backends(self    ,			['flax']       )



      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Optional[Any]    ,			*SCREAMING_SNAKE_CASE_				:      str    ,			**SCREAMING_SNAKE_CASE_				:      List[str]       ):
        requires_backends(cls    ,			['flax']       )





      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      List[str]    ,			*SCREAMING_SNAKE_CASE_				:      Optional[int]    ,			**SCREAMING_SNAKE_CASE_				:      Dict       ):
        requires_backends(cls    ,			['flax']       )







class       UpperCamelCase__   (	metaclass=lowercase_  ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE  				=     ["""flax"""]



      def __init__(      self				:      Any    ,			*SCREAMING_SNAKE_CASE_				:      int    ,			**SCREAMING_SNAKE_CASE_				:      Dict       ):
        requires_backends(self    ,			['flax']       )



      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      str    ,			*SCREAMING_SNAKE_CASE_				:      Optional[Any]    ,			**SCREAMING_SNAKE_CASE_				:      Any       ):
        requires_backends(cls    ,			['flax']       )





      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Tuple    ,			*SCREAMING_SNAKE_CASE_				:      List[Any]    ,			**SCREAMING_SNAKE_CASE_				:      Union[str, Any]       ):
        requires_backends(cls    ,			['flax']       )







class       UpperCamelCase__   (	metaclass=lowercase_  ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE  				=     ["""flax"""]



      def __init__(      self				:      Tuple    ,			*SCREAMING_SNAKE_CASE_				:      Any    ,			**SCREAMING_SNAKE_CASE_				:      Optional[Any]       ):
        requires_backends(self    ,			['flax']       )



      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Optional[int]    ,			*SCREAMING_SNAKE_CASE_				:      int    ,			**SCREAMING_SNAKE_CASE_				:      Dict       ):
        requires_backends(cls    ,			['flax']       )





      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Optional[int]    ,			*SCREAMING_SNAKE_CASE_				:      Tuple    ,			**SCREAMING_SNAKE_CASE_				:      Union[str, Any]       ):
        requires_backends(cls    ,			['flax']       )







class       UpperCamelCase__   (	metaclass=lowercase_  ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE  				=     ["""flax"""]



      def __init__(      self				:      int    ,			*SCREAMING_SNAKE_CASE_				:      int    ,			**SCREAMING_SNAKE_CASE_				:      Union[str, Any]       ):
        requires_backends(self    ,			['flax']       )



      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Union[str, Any]    ,			*SCREAMING_SNAKE_CASE_				:      List[str]    ,			**SCREAMING_SNAKE_CASE_				:      Tuple       ):
        requires_backends(cls    ,			['flax']       )





      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Dict    ,			*SCREAMING_SNAKE_CASE_				:      List[Any]    ,			**SCREAMING_SNAKE_CASE_				:      Tuple       ):
        requires_backends(cls    ,			['flax']       )







class       UpperCamelCase__   (	metaclass=lowercase_  ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE  				=     ["""flax"""]



      def __init__(      self				:      Union[str, Any]    ,			*SCREAMING_SNAKE_CASE_				:      int    ,			**SCREAMING_SNAKE_CASE_				:      Dict       ):
        requires_backends(self    ,			['flax']       )



      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Any    ,			*SCREAMING_SNAKE_CASE_				:      Optional[int]    ,			**SCREAMING_SNAKE_CASE_				:      str       ):
        requires_backends(cls    ,			['flax']       )





      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Dict    ,			*SCREAMING_SNAKE_CASE_				:      List[Any]    ,			**SCREAMING_SNAKE_CASE_				:      Tuple       ):
        requires_backends(cls    ,			['flax']       )







class       UpperCamelCase__   (	metaclass=lowercase_  ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE  				=     ["""flax"""]



      def __init__(      self				:      Dict    ,			*SCREAMING_SNAKE_CASE_				:      List[Any]    ,			**SCREAMING_SNAKE_CASE_				:      List[Any]       ):
        requires_backends(self    ,			['flax']       )



      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Optional[int]    ,			*SCREAMING_SNAKE_CASE_				:      Tuple    ,			**SCREAMING_SNAKE_CASE_				:      List[Any]       ):
        requires_backends(cls    ,			['flax']       )





      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Dict    ,			*SCREAMING_SNAKE_CASE_				:      Optional[Any]    ,			**SCREAMING_SNAKE_CASE_				:      int       ):
        requires_backends(cls    ,			['flax']       )







class       UpperCamelCase__   (	metaclass=lowercase_  ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE  				=     ["""flax"""]



      def __init__(      self				:      Optional[int]    ,			*SCREAMING_SNAKE_CASE_				:      List[Any]    ,			**SCREAMING_SNAKE_CASE_				:      Dict       ):
        requires_backends(self    ,			['flax']       )



      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Optional[Any]    ,			*SCREAMING_SNAKE_CASE_				:      Union[str, Any]    ,			**SCREAMING_SNAKE_CASE_				:      Optional[Any]       ):
        requires_backends(cls    ,			['flax']       )





      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Union[str, Any]    ,			*SCREAMING_SNAKE_CASE_				:      Optional[Any]    ,			**SCREAMING_SNAKE_CASE_				:      int       ):
        requires_backends(cls    ,			['flax']       )







class       UpperCamelCase__   (	metaclass=lowercase_  ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE  				=     ["""flax"""]



      def __init__(      self				:      Tuple    ,			*SCREAMING_SNAKE_CASE_				:      Any    ,			**SCREAMING_SNAKE_CASE_				:      Any       ):
        requires_backends(self    ,			['flax']       )



      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Union[str, Any]    ,			*SCREAMING_SNAKE_CASE_				:      Tuple    ,			**SCREAMING_SNAKE_CASE_				:      List[str]       ):
        requires_backends(cls    ,			['flax']       )





      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Tuple    ,			*SCREAMING_SNAKE_CASE_				:      Optional[Any]    ,			**SCREAMING_SNAKE_CASE_				:      str       ):
        requires_backends(cls    ,			['flax']       )







class       UpperCamelCase__   (	metaclass=lowercase_  ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE  				=     ["""flax"""]



      def __init__(      self				:      Optional[Any]    ,			*SCREAMING_SNAKE_CASE_				:      Any    ,			**SCREAMING_SNAKE_CASE_				:      int       ):
        requires_backends(self    ,			['flax']       )



      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Tuple    ,			*SCREAMING_SNAKE_CASE_				:      Dict    ,			**SCREAMING_SNAKE_CASE_				:      Optional[int]       ):
        requires_backends(cls    ,			['flax']       )





      @classmethod
      def      SCREAMING_SNAKE_CASE__ (      cls				:      Optional[int]    ,			*SCREAMING_SNAKE_CASE_				:      str    ,			**SCREAMING_SNAKE_CASE_				:      Tuple       ):
        requires_backends(cls    ,			['flax']       )





