


from ..utils import DummyObject, requires_backends


class 			_a				(     metaclass=UpperCamelCase__     ):
							_lowercase      :     Dict     =					['''flax''', '''transformers''']

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





									"""simple docstring"""







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

							@classmethod
							def  lowerCamelCase_					(				cls:      Optional[Any]       ,		*UpperCamelCase_:      Dict       ,		**UpperCamelCase_:      Tuple				)     ->  str:





									"""simple docstring"""







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


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





									"""simple docstring"""







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


class 			_a				(     metaclass=UpperCamelCase__     ):
							_lowercase      :     str     =					['''flax''', '''transformers''']

							def __init__(				self:      Dict       ,		*UpperCamelCase_:      str       ,		**UpperCamelCase_:      Dict				)     ->  Dict:





									"""simple docstring"""







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

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





									"""simple docstring"""







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


							@classmethod
							def  lowerCamelCase_					(				cls:      Tuple       ,		*UpperCamelCase_:      List[Any]       ,		**UpperCamelCase_:      int				)     ->  Any:





									"""simple docstring"""







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


class 			_a				(     metaclass=UpperCamelCase__     ):
							_lowercase      :     Dict     =					['''flax''', '''transformers''']

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





									"""simple docstring"""







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

							@classmethod
							def  lowerCamelCase_					(				cls:      Optional[Any]       ,		*UpperCamelCase_:      Tuple       ,		**UpperCamelCase_:      Any				)     ->  Tuple:





									"""simple docstring"""







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


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





									"""simple docstring"""







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


class 			_a				(     metaclass=UpperCamelCase__     ):
							_lowercase      :     Union[str, Any]     =					['''flax''', '''transformers''']

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





									"""simple docstring"""







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

							@classmethod
							def  lowerCamelCase_					(				cls:      int       ,		*UpperCamelCase_:      Optional[int]       ,		**UpperCamelCase_:      Any				)     ->  Optional[Any]:





									"""simple docstring"""







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


							@classmethod
							def  lowerCamelCase_					(				cls:      Any       ,		*UpperCamelCase_:      Union[str, Any]       ,		**UpperCamelCase_:      Optional[int]				)     ->  Any:





									"""simple docstring"""







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








from __future__ import annotations

from fractions import Fraction




def 		lowerCAmelCase_ (						lowerCamelCase						,  lowerCamelCase ):
				return (
				    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
				)




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						List[str]										=[]
				__magic_name__						:						List[Any]										=11
				__magic_name__						:						Tuple										=int("""1""" + """0""" * digit_len )
				for num in range(lowerCamelCase						,  lowerCamelCase ):
								while den <= 99:
												if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
																if is_digit_cancelling(lowerCamelCase						,  lowerCamelCase ):
																				solutions.append(F"{num}/{den}" )
												den += 1
								num += 1
								__magic_name__						:						List[str]										=10
				return solutions




def 		lowerCAmelCase_ (						lowerCamelCase = 2 ):
				__magic_name__						:						str										=1.0
				for fraction in fraction_list(lowerCamelCase ):
								__magic_name__						:						int										=Fraction(lowerCamelCase )
								result *= frac.denominator / frac.numerator
				return int(lowerCamelCase )


if __name__ == "__main__":
							print(solution())




