




from ..utils import DummyObject, requires_backends
class 						_A (  metaclass=_lowerCamelCase				):
  _UpperCamelCase       :      List[str]			=      ['''flax''']






  def __init__(  self		:     str				,						*_A		:     Optional[Any]				,						**_A		:     Any				)		->   Optional[int]:






       """simple docstring"""







       requires_backends(self				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     str				,						*_A		:     Union[str, Any]				,						**_A		:     Dict				)		->   List[str]:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     int				,						*_A		:     Dict				,						**_A		:     Any				)		->   List[str]:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)


class 						_A (  metaclass=_lowerCamelCase				):
  _UpperCamelCase       :      Tuple			=      ['''flax''']






  def __init__(  self		:     Dict				,						*_A		:     Optional[int]				,						**_A		:     Dict				)		->   Tuple:






       """simple docstring"""







       requires_backends(self				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     Optional[Any]				,						*_A		:     Optional[int]				,						**_A		:     List[Any]				)		->   str:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     Dict				,						*_A		:     Any				,						**_A		:     Optional[int]				)		->   List[Any]:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)


class 						_A (  metaclass=_lowerCamelCase				):
  _UpperCamelCase       :      Union[str, Any]			=      ['''flax''']






  def __init__(  self		:     str				,						*_A		:     Any				,						**_A		:     Any				)		->   Any:






       """simple docstring"""







       requires_backends(self				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     Union[str, Any]				,						*_A		:     Optional[int]				,						**_A		:     Optional[int]				)		->   Dict:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     int				,						*_A		:     Optional[Any]				,						**_A		:     List[Any]				)		->   Optional[Any]:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)


class 						_A (  metaclass=_lowerCamelCase				):
  _UpperCamelCase       :      Optional[int]			=      ['''flax''']






  def __init__(  self		:     List[Any]				,						*_A		:     Dict				,						**_A		:     Optional[int]				)		->   Tuple:






       """simple docstring"""







       requires_backends(self				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     Union[str, Any]				,						*_A		:     Dict				,						**_A		:     int				)		->   Optional[Any]:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     List[Any]				,						*_A		:     Union[str, Any]				,						**_A		:     Dict				)		->   Tuple:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)


class 						_A (  metaclass=_lowerCamelCase				):
  _UpperCamelCase       :      Optional[int]			=      ['''flax''']






  def __init__(  self		:     int				,						*_A		:     int				,						**_A		:     int				)		->   int:






       """simple docstring"""







       requires_backends(self				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     List[Any]				,						*_A		:     List[Any]				,						**_A		:     Dict				)		->   Union[str, Any]:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     Union[str, Any]				,						*_A		:     Any				,						**_A		:     List[Any]				)		->   str:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)


class 						_A (  metaclass=_lowerCamelCase				):
  _UpperCamelCase       :      str			=      ['''flax''']






  def __init__(  self		:     Dict				,						*_A		:     List[Any]				,						**_A		:     Dict				)		->   str:






       """simple docstring"""







       requires_backends(self				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     Optional[int]				,						*_A		:     str				,						**_A		:     List[str]				)		->   Optional[int]:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     int				,						*_A		:     List[Any]				,						**_A		:     List[str]				)		->   Optional[int]:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)


class 						_A (  metaclass=_lowerCamelCase				):
  _UpperCamelCase       :      List[Any]			=      ['''flax''']






  def __init__(  self		:     List[str]				,						*_A		:     Dict				,						**_A		:     Any				)		->   Union[str, Any]:






       """simple docstring"""







       requires_backends(self				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     int				,						*_A		:     Dict				,						**_A		:     Optional[Any]				)		->   int:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     str				,						*_A		:     List[str]				,						**_A		:     Dict				)		->   Tuple:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)


class 						_A (  metaclass=_lowerCamelCase				):
  _UpperCamelCase       :      Optional[Any]			=      ['''flax''']






  def __init__(  self		:     int				,						*_A		:     List[Any]				,						**_A		:     Optional[Any]				)		->   Tuple:






       """simple docstring"""







       requires_backends(self				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     Union[str, Any]				,						*_A		:     Dict				,						**_A		:     List[Any]				)		->   Any:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     int				,						*_A		:     Tuple				,						**_A		:     List[str]				)		->   List[str]:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)


class 						_A (  metaclass=_lowerCamelCase				):
  _UpperCamelCase       :      Union[str, Any]			=      ['''flax''']






  def __init__(  self		:     Any				,						*_A		:     Optional[int]				,						**_A		:     Any				)		->   Union[str, Any]:






       """simple docstring"""







       requires_backends(self				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     Tuple				,						*_A		:     Dict				,						**_A		:     int				)		->   str:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     Union[str, Any]				,						*_A		:     Dict				,						**_A		:     int				)		->   Any:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)


class 						_A (  metaclass=_lowerCamelCase				):
  _UpperCamelCase       :      Optional[Any]			=      ['''flax''']






  def __init__(  self		:     Optional[Any]				,						*_A		:     Any				,						**_A		:     Any				)		->   Any:






       """simple docstring"""







       requires_backends(self				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     Optional[int]				,						*_A		:     Union[str, Any]				,						**_A		:     Optional[int]				)		->   List[Any]:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     str				,						*_A		:     Union[str, Any]				,						**_A		:     List[str]				)		->   Dict:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)


class 						_A (  metaclass=_lowerCamelCase				):
  _UpperCamelCase       :      Union[str, Any]			=      ['''flax''']






  def __init__(  self		:     List[Any]				,						*_A		:     Tuple				,						**_A		:     Dict				)		->   List[Any]:






       """simple docstring"""







       requires_backends(self				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     List[str]				,						*_A		:     Tuple				,						**_A		:     Any				)		->   Optional[Any]:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     Union[str, Any]				,						*_A		:     List[Any]				,						**_A		:     Any				)		->   Union[str, Any]:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)


class 						_A (  metaclass=_lowerCamelCase				):
  _UpperCamelCase       :      Tuple			=      ['''flax''']






  def __init__(  self		:     Union[str, Any]				,						*_A		:     Optional[Any]				,						**_A		:     int				)		->   Optional[int]:






       """simple docstring"""







       requires_backends(self				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     Union[str, Any]				,						*_A		:     Optional[int]				,						**_A		:     int				)		->   List[str]:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     Optional[Any]				,						*_A		:     Optional[int]				,						**_A		:     Optional[int]				)		->   Tuple:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)


class 						_A (  metaclass=_lowerCamelCase				):
  _UpperCamelCase       :      List[Any]			=      ['''flax''']






  def __init__(  self		:     Optional[int]				,						*_A		:     Tuple				,						**_A		:     int				)		->   Any:






       """simple docstring"""







       requires_backends(self				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     Optional[Any]				,						*_A		:     List[Any]				,						**_A		:     int				)		->   Tuple:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)






  @classmethod
  def  __a      (  cls		:     List[str]				,						*_A		:     List[Any]				,						**_A		:     str				)		->   Optional[int]:






       """simple docstring"""







       requires_backends(cls				,						['''flax''']				)





import math






def  snake_case(    __magic_name__   )			->							bool:





     '''simple docstring'''


     lowercase :       Union[str, Any]       =			math.loga(math.sqrt(4 * positive_integer + 1   ) / 2 + 1 / 2   )

     return exponent == int(__magic_name__   )






def  snake_case(    __magic_name__ = 1 / 1_23_45   )			->							int:





     '''simple docstring'''


     lowercase :       Union[str, Any]       =			0
     lowercase :       str       =			0

     lowercase :       Optional[int]       =			3
     while True:
          lowercase :       Any       =			(integer**2 - 1) / 4
          # if candidate is an integer, then there is a partition for k
          if partition_candidate == int(__magic_name__   ):
               lowercase :       Any       =			int(__magic_name__   )
               total_partitions += 1
               if check_partition_perfect(__magic_name__   ):
                    perfect_partitions += 1
          if perfect_partitions > 0:
               if perfect_partitions / total_partitions < max_proportion:
                    return int(__magic_name__   )
          integer += 1


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