


'''simple docstring'''


from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt





def       lowerCAmelCase					(		UpperCamelCase__				:   int       ):


	"""simple docstring"""
	__UpperCAmelCase							=			int(number**0.5       )
	return number == sq * sq





def       lowerCAmelCase					(		UpperCamelCase__				:   int    ,					UpperCamelCase__				:   int    ,					UpperCamelCase__				:   int    ,					UpperCamelCase__				:   int    ,					UpperCamelCase__				:   int    ,					UpperCamelCase__				:   int       ):


	"""simple docstring"""
	__UpperCAmelCase							=			x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
	__UpperCAmelCase							=			x_den * y_den * z_den
	__UpperCAmelCase							=			gcd(lowerCamelCase_    ,					lowerCamelCase_       )
	top //= hcf
	bottom //= hcf
	return top, bottom





def       lowerCAmelCase					(		UpperCamelCase__				:   int = 3_5       ):


	"""simple docstring"""
	__UpperCAmelCase							=			set()
	__UpperCAmelCase							=			4_2
	__UpperCAmelCase							=			Fraction(0       )
	__UpperCAmelCase							=			4_2

	for x_num in range(1    ,					order + 1       ):
		for x_den in range(x_num + 1    ,					order + 1       ):
			for y_num in range(1    ,					order + 1       ):
				for y_den in range(y_num + 1    ,					order + 1       ):
					# n=1
					__UpperCAmelCase							=			x_num * y_den + x_den * y_num
					__UpperCAmelCase							=			x_den * y_den
					__UpperCAmelCase							=			gcd(lowerCamelCase_    ,					lowerCamelCase_       )
					z_num //= hcf
					z_den //= hcf
					if 0 < z_num < z_den <= order:
						__UpperCAmelCase							=			add_three(
						    lowerCamelCase_    ,					lowerCamelCase_    ,					lowerCamelCase_    ,					lowerCamelCase_    ,					lowerCamelCase_    ,					lowerCamelCase_       )
						unique_s.add(lowerCamelCase_       )

					# n=2
					__UpperCAmelCase							=			(
					    x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
					)
					__UpperCAmelCase							=			x_den * x_den * y_den * y_den
					if is_sq(lowerCamelCase_       ) and is_sq(lowerCamelCase_       ):
						__UpperCAmelCase							=			int(sqrt(lowerCamelCase_       )       )
						__UpperCAmelCase							=			int(sqrt(lowerCamelCase_       )       )
						__UpperCAmelCase							=			gcd(lowerCamelCase_    ,					lowerCamelCase_       )
						z_num //= hcf
						z_den //= hcf
						if 0 < z_num < z_den <= order:
							__UpperCAmelCase							=			add_three(
							    lowerCamelCase_    ,					lowerCamelCase_    ,					lowerCamelCase_    ,					lowerCamelCase_    ,					lowerCamelCase_    ,					lowerCamelCase_       )
							unique_s.add(lowerCamelCase_       )

                    # n=-1
					__UpperCAmelCase							=			x_num * y_num
					__UpperCAmelCase							=			x_den * y_num + x_num * y_den
					__UpperCAmelCase							=			gcd(lowerCamelCase_    ,					lowerCamelCase_       )
					z_num //= hcf
					z_den //= hcf
					if 0 < z_num < z_den <= order:
						__UpperCAmelCase							=			add_three(
						    lowerCamelCase_    ,					lowerCamelCase_    ,					lowerCamelCase_    ,					lowerCamelCase_    ,					lowerCamelCase_    ,					lowerCamelCase_       )
						unique_s.add(lowerCamelCase_       )

					# n=2
					__UpperCAmelCase							=			x_num * x_num * y_num * y_num
					__UpperCAmelCase							=			(
					    x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
					)
					if is_sq(lowerCamelCase_       ) and is_sq(lowerCamelCase_       ):
						__UpperCAmelCase							=			int(sqrt(lowerCamelCase_       )       )
						__UpperCAmelCase							=			int(sqrt(lowerCamelCase_       )       )
						__UpperCAmelCase							=			gcd(lowerCamelCase_    ,					lowerCamelCase_       )
						z_num //= hcf
						z_den //= hcf
						if 0 < z_num < z_den <= order:
							__UpperCAmelCase							=			add_three(
							    lowerCamelCase_    ,					lowerCamelCase_    ,					lowerCamelCase_    ,					lowerCamelCase_    ,					lowerCamelCase_    ,					lowerCamelCase_       )
							unique_s.add(lowerCamelCase_       )

	for num, den in unique_s:
		total += Fraction(lowerCamelCase_    ,					lowerCamelCase_       )

	return total.denominator + total.numerator


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

'''simple docstring'''


from ..utils import DummyObject, requires_backends






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Optional[int]     ,		*__a				:							List[str]     ,		**__a				:							Union[str, Any]	)							->	Union[str, Any]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Any     ,		*__a				:							List[str]     ,		**__a				:							int	)							->	Dict:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							List[str]     ,		*__a				:							int     ,		**__a				:							List[Any]	)							->	Tuple:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							int     ,		*__a				:							Optional[Any]     ,		**__a				:							Tuple	)							->	Dict:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Optional[Any]     ,		*__a				:							Tuple     ,		**__a				:							Optional[Any]	)							->	int:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Dict     ,		*__a				:							str     ,		**__a				:							Tuple	)							->	Optional[Any]:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Any     ,		*__a				:							List[str]     ,		**__a				:							int	)							->	Optional[Any]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							List[str]     ,		*__a				:							List[str]     ,		**__a				:							Optional[int]	)							->	List[Any]:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Any     ,		*__a				:							str     ,		**__a				:							Any	)							->	Tuple:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							List[str]     ,		*__a				:							Dict     ,		**__a				:							List[str]	)							->	List[str]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Dict     ,		*__a				:							Any     ,		**__a				:							List[Any]	)							->	Union[str, Any]:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							str     ,		*__a				:							List[str]     ,		**__a				:							Union[str, Any]	)							->	List[str]:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							str     ,		*__a				:							Optional[int]     ,		**__a				:							Optional[int]	)							->	Any:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Optional[Any]     ,		*__a				:							Dict     ,		**__a				:							List[Any]	)							->	str:
								requires_backends(cls     ,		['''torch''']	)






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






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Dict     ,		*__a				:							Optional[Any]     ,		**__a				:							int	)							->	Union[str, Any]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							int     ,		*__a				:							Optional[int]     ,		**__a				:							Dict	)							->	Dict:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							List[str]     ,		*__a				:							Tuple     ,		**__a				:							Any	)							->	List[str]:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Optional[Any]     ,		*__a				:							Optional[Any]     ,		**__a				:							int	)							->	List[str]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							List[str]     ,		*__a				:							Tuple     ,		**__a				:							Optional[int]	)							->	Tuple:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Any     ,		*__a				:							str     ,		**__a				:							List[Any]	)							->	Optional[Any]:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Dict     ,		*__a				:							List[Any]     ,		**__a				:							int	)							->	List[str]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Union[str, Any]     ,		*__a				:							int     ,		**__a				:							str	)							->	List[Any]:
								requires_backends(cls     ,		['''torch''']	)






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






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Tuple     ,		*__a				:							str     ,		**__a				:							Tuple	)							->	Dict:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							str     ,		*__a				:							List[str]     ,		**__a				:							Optional[Any]	)							->	str:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Tuple     ,		*__a				:							Optional[int]     ,		**__a				:							Union[str, Any]	)							->	int:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Any     ,		*__a				:							Union[str, Any]     ,		**__a				:							List[str]	)							->	str:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Union[str, Any]     ,		*__a				:							Dict     ,		**__a				:							Union[str, Any]	)							->	List[Any]:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Any     ,		*__a				:							Union[str, Any]     ,		**__a				:							Any	)							->	List[str]:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							str     ,		*__a				:							int     ,		**__a				:							int	)							->	List[str]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							List[str]     ,		*__a				:							Optional[int]     ,		**__a				:							int	)							->	Dict:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Dict     ,		*__a				:							Tuple     ,		**__a				:							str	)							->	Dict:
								requires_backends(cls     ,		['''torch''']	)





def       lowerCAmelCase					(		*UpperCamelCase__				:   int    ,					**UpperCamelCase__				:   Optional[int]       ):


	"""simple docstring"""
	requires_backends(UpperCamelCase__    ,					['''torch''']       )





def       lowerCAmelCase					(		*UpperCamelCase__				:   Optional[int]    ,					**UpperCamelCase__				:   List[Any]       ):


	"""simple docstring"""
	requires_backends(UpperCamelCase__    ,					['''torch''']       )





def       lowerCAmelCase					(		*UpperCamelCase__				:   Any    ,					**UpperCamelCase__				:   List[str]       ):


	"""simple docstring"""
	requires_backends(UpperCamelCase__    ,					['''torch''']       )





def       lowerCAmelCase					(		*UpperCamelCase__				:   str    ,					**UpperCamelCase__				:   str       ):


	"""simple docstring"""
	requires_backends(UpperCamelCase__    ,					['''torch''']       )





def       lowerCAmelCase					(		*UpperCamelCase__				:   Dict    ,					**UpperCamelCase__				:   Dict       ):


	"""simple docstring"""
	requires_backends(UpperCamelCase__    ,					['''torch''']       )





def       lowerCAmelCase					(		*UpperCamelCase__				:   Tuple    ,					**UpperCamelCase__				:   int       ):


	"""simple docstring"""
	requires_backends(UpperCamelCase__    ,					['''torch''']       )





def       lowerCAmelCase					(		*UpperCamelCase__				:   Union[str, Any]    ,					**UpperCamelCase__				:   Tuple       ):


	"""simple docstring"""
	requires_backends(UpperCamelCase__    ,					['''torch''']       )






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Union[str, Any]     ,		*__a				:							str     ,		**__a				:							List[Any]	)							->	Any:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							str     ,		*__a				:							int     ,		**__a				:							int	)							->	Any:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Optional[Any]     ,		*__a				:							Dict     ,		**__a				:							List[str]	)							->	Any:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Optional[Any]     ,		*__a				:							str     ,		**__a				:							List[str]	)							->	Optional[Any]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Union[str, Any]     ,		*__a				:							Dict     ,		**__a				:							Tuple	)							->	int:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Optional[Any]     ,		*__a				:							List[Any]     ,		**__a				:							List[str]	)							->	Any:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Optional[Any]     ,		*__a				:							List[Any]     ,		**__a				:							List[Any]	)							->	int:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Any     ,		*__a				:							Tuple     ,		**__a				:							int	)							->	Union[str, Any]:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Tuple     ,		*__a				:							Any     ,		**__a				:							int	)							->	Optional[Any]:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Any     ,		*__a				:							Optional[Any]     ,		**__a				:							Tuple	)							->	List[Any]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Optional[int]     ,		*__a				:							str     ,		**__a				:							int	)							->	Any:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							List[str]     ,		*__a				:							Dict     ,		**__a				:							Any	)							->	str:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Any     ,		*__a				:							str     ,		**__a				:							str	)							->	List[Any]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							List[str]     ,		*__a				:							Union[str, Any]     ,		**__a				:							str	)							->	Union[str, Any]:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							List[str]     ,		*__a				:							int     ,		**__a				:							Tuple	)							->	str:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Optional[int]     ,		*__a				:							Tuple     ,		**__a				:							str	)							->	Union[str, Any]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Tuple     ,		*__a				:							Any     ,		**__a				:							Dict	)							->	Dict:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Union[str, Any]     ,		*__a				:							str     ,		**__a				:							List[str]	)							->	str:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Any     ,		*__a				:							int     ,		**__a				:							int	)							->	Union[str, Any]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							int     ,		*__a				:							str     ,		**__a				:							List[Any]	)							->	Union[str, Any]:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Tuple     ,		*__a				:							int     ,		**__a				:							List[str]	)							->	Optional[Any]:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							int     ,		*__a				:							Union[str, Any]     ,		**__a				:							Optional[Any]	)							->	Any:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Tuple     ,		*__a				:							List[Any]     ,		**__a				:							str	)							->	int:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							int     ,		*__a				:							Optional[Any]     ,		**__a				:							Any	)							->	Dict:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							List[str]     ,		*__a				:							List[str]     ,		**__a				:							Dict	)							->	Optional[int]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Optional[Any]     ,		*__a				:							Union[str, Any]     ,		**__a				:							Optional[int]	)							->	Tuple:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							List[Any]     ,		*__a				:							int     ,		**__a				:							Dict	)							->	Tuple:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							List[str]     ,		*__a				:							List[str]     ,		**__a				:							Union[str, Any]	)							->	str:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Union[str, Any]     ,		*__a				:							int     ,		**__a				:							Dict	)							->	List[Any]:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Tuple     ,		*__a				:							Tuple     ,		**__a				:							List[str]	)							->	Any:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Any     ,		*__a				:							str     ,		**__a				:							Any	)							->	int:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							str     ,		*__a				:							Dict     ,		**__a				:							Optional[Any]	)							->	Any:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Any     ,		*__a				:							str     ,		**__a				:							Union[str, Any]	)							->	Tuple:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Any     ,		*__a				:							Optional[Any]     ,		**__a				:							List[str]	)							->	str:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Union[str, Any]     ,		*__a				:							Union[str, Any]     ,		**__a				:							Any	)							->	Any:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Tuple     ,		*__a				:							Union[str, Any]     ,		**__a				:							List[Any]	)							->	Optional[Any]:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Tuple     ,		*__a				:							Optional[int]     ,		**__a				:							List[Any]	)							->	Any:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Tuple     ,		*__a				:							List[str]     ,		**__a				:							Dict	)							->	List[str]:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Optional[int]     ,		*__a				:							Optional[Any]     ,		**__a				:							List[Any]	)							->	Any:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Optional[int]     ,		*__a				:							Any     ,		**__a				:							str	)							->	List[Any]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Optional[int]     ,		*__a				:							Optional[Any]     ,		**__a				:							int	)							->	Union[str, Any]:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Optional[Any]     ,		*__a				:							int     ,		**__a				:							Optional[Any]	)							->	int:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							str     ,		*__a				:							List[str]     ,		**__a				:							Dict	)							->	List[str]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Tuple     ,		*__a				:							Any     ,		**__a				:							Union[str, Any]	)							->	Optional[int]:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Optional[Any]     ,		*__a				:							Dict     ,		**__a				:							Union[str, Any]	)							->	List[str]:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Any     ,		*__a				:							Tuple     ,		**__a				:							Optional[int]	)							->	str:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Dict     ,		*__a				:							List[Any]     ,		**__a				:							List[str]	)							->	Any:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							List[str]     ,		*__a				:							Union[str, Any]     ,		**__a				:							Union[str, Any]	)							->	Any:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Dict     ,		*__a				:							List[Any]     ,		**__a				:							int	)							->	int:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							List[str]     ,		*__a				:							Optional[Any]     ,		**__a				:							str	)							->	int:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Any     ,		*__a				:							Tuple     ,		**__a				:							int	)							->	Any:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Optional[Any]     ,		*__a				:							Optional[int]     ,		**__a				:							Tuple	)							->	Optional[int]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							int     ,		*__a				:							Union[str, Any]     ,		**__a				:							List[Any]	)							->	Dict:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							int     ,		*__a				:							List[Any]     ,		**__a				:							List[str]	)							->	str:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							List[Any]     ,		*__a				:							Optional[int]     ,		**__a				:							int	)							->	Dict:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							List[str]     ,		*__a				:							Union[str, Any]     ,		**__a				:							List[Any]	)							->	Optional[Any]:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Any     ,		*__a				:							int     ,		**__a				:							Any	)							->	str:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							str     ,		*__a				:							Any     ,		**__a				:							int	)							->	Tuple:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Union[str, Any]     ,		*__a				:							List[Any]     ,		**__a				:							Union[str, Any]	)							->	Union[str, Any]:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Optional[int]     ,		*__a				:							List[Any]     ,		**__a				:							Dict	)							->	int:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							List[Any]     ,		*__a				:							int     ,		**__a				:							Optional[int]	)							->	List[str]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Dict     ,		*__a				:							List[Any]     ,		**__a				:							Any	)							->	str:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Dict     ,		*__a				:							Tuple     ,		**__a				:							List[Any]	)							->	Any:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Dict     ,		*__a				:							Dict     ,		**__a				:							Optional[int]	)							->	Dict:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Optional[int]     ,		*__a				:							Any     ,		**__a				:							Dict	)							->	Tuple:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							str     ,		*__a				:							Any     ,		**__a				:							Any	)							->	Optional[Any]:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Union[str, Any]     ,		*__a				:							Tuple     ,		**__a				:							Optional[int]	)							->	Optional[Any]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							str     ,		*__a				:							Optional[Any]     ,		**__a				:							Optional[Any]	)							->	str:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Optional[Any]     ,		*__a				:							List[Any]     ,		**__a				:							Dict	)							->	Union[str, Any]:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Dict     ,		*__a				:							Union[str, Any]     ,		**__a				:							Optional[int]	)							->	Dict:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Union[str, Any]     ,		*__a				:							Any     ,		**__a				:							Optional[int]	)							->	Optional[int]:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Dict     ,		*__a				:							Union[str, Any]     ,		**__a				:							List[str]	)							->	Optional[Any]:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Optional[Any]     ,		*__a				:							Optional[int]     ,		**__a				:							List[Any]	)							->	str:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Any     ,		*__a				:							Dict     ,		**__a				:							int	)							->	Optional[Any]:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							List[str]     ,		*__a				:							Optional[int]     ,		**__a				:							Union[str, Any]	)							->	Dict:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Optional[int]     ,		*__a				:							Union[str, Any]     ,		**__a				:							int	)							->	Optional[int]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							List[Any]     ,		*__a				:							Optional[Any]     ,		**__a				:							int	)							->	Tuple:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							List[Any]     ,		*__a				:							List[Any]     ,		**__a				:							Optional[int]	)							->	Optional[int]:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Optional[int]     ,		*__a				:							Optional[Any]     ,		**__a				:							Optional[int]	)							->	Tuple:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Optional[int]     ,		*__a				:							Optional[int]     ,		**__a				:							List[Any]	)							->	Dict:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							int     ,		*__a				:							List[str]     ,		**__a				:							Union[str, Any]	)							->	Tuple:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							str     ,		*__a				:							Tuple     ,		**__a				:							Tuple	)							->	str:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							List[Any]     ,		*__a				:							List[str]     ,		**__a				:							Tuple	)							->	Tuple:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Union[str, Any]     ,		*__a				:							Dict     ,		**__a				:							Tuple	)							->	Tuple:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Optional[Any]     ,		*__a				:							Union[str, Any]     ,		**__a				:							Optional[int]	)							->	List[Any]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Dict     ,		*__a				:							List[str]     ,		**__a				:							int	)							->	str:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							int     ,		*__a				:							Tuple     ,		**__a				:							Optional[Any]	)							->	Optional[Any]:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Optional[int]     ,		*__a				:							Union[str, Any]     ,		**__a				:							Union[str, Any]	)							->	Optional[int]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Optional[Any]     ,		*__a				:							Any     ,		**__a				:							List[str]	)							->	str:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							str     ,		*__a				:							int     ,		**__a				:							int	)							->	List[Any]:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Dict     ,		*__a				:							Any     ,		**__a				:							List[Any]	)							->	Union[str, Any]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Dict     ,		*__a				:							int     ,		**__a				:							str	)							->	Any:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							List[Any]     ,		*__a				:							Dict     ,		**__a				:							Optional[Any]	)							->	Dict:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Union[str, Any]     ,		*__a				:							List[str]     ,		**__a				:							int	)							->	Union[str, Any]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Union[str, Any]     ,		*__a				:							List[Any]     ,		**__a				:							Any	)							->	int:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							List[str]     ,		*__a				:							str     ,		**__a				:							Optional[Any]	)							->	Dict:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Optional[int]     ,		*__a				:							List[Any]     ,		**__a				:							List[str]	)							->	Optional[int]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Union[str, Any]     ,		*__a				:							Optional[Any]     ,		**__a				:							str	)							->	int:
								requires_backends(cls     ,		['''torch''']	)






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






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Union[str, Any]     ,		*__a				:							List[Any]     ,		**__a				:							Optional[Any]	)							->	int:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Union[str, Any]     ,		*__a				:							List[Any]     ,		**__a				:							Any	)							->	int:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Optional[Any]     ,		*__a				:							List[str]     ,		**__a				:							Any	)							->	str:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Any     ,		*__a				:							List[str]     ,		**__a				:							Dict	)							->	List[str]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							List[Any]     ,		*__a				:							Dict     ,		**__a				:							Optional[Any]	)							->	Union[str, Any]:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							List[Any]     ,		*__a				:							str     ,		**__a				:							Any	)							->	Dict:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							List[str]     ,		*__a				:							Union[str, Any]     ,		**__a				:							Optional[int]	)							->	List[Any]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							str     ,		*__a				:							Dict     ,		**__a				:							Tuple	)							->	Optional[int]:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							str     ,		*__a				:							Any     ,		**__a				:							Any	)							->	Any:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							int     ,		*__a				:							Any     ,		**__a				:							Optional[Any]	)							->	int:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							Dict     ,		*__a				:							int     ,		**__a				:							List[Any]	)							->	str:
								requires_backends(cls     ,		['''torch''']	)






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






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Tuple     ,		*__a				:							int     ,		**__a				:							Optional[Any]	)							->	List[Any]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							List[Any]     ,		*__a				:							Union[str, Any]     ,		**__a				:							Union[str, Any]	)							->	str:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							Tuple     ,		*__a				:							Any     ,		**__a				:							Optional[int]	)							->	str:
								requires_backends(cls     ,		['''torch''']	)






class 						A   (   metaclass=UpperCAmelCase   ):
							a_        =      ['''torch''']





							def __init__(      self				:							Dict     ,		*__a				:							List[str]     ,		**__a				:							List[Any]	)							->	Optional[Any]:
								requires_backends(self     ,		['''torch''']	)





							@classmethod
							def       snake_case__						(      cls				:							List[Any]     ,		*__a				:							int     ,		**__a				:							Any	)							->	Any:
								requires_backends(cls     ,		['''torch''']	)






							@classmethod
							def       snake_case__						(      cls				:							List[Any]     ,		*__a				:							List[str]     ,		**__a				:							List[str]	)							->	List[Any]:
								requires_backends(cls     ,		['''torch''']	)
