
"""simple docstring"""






def __A						(   a_ :							int		,		a_ :							int     )->							str:




		'''simple docstring'''






		if a < 0 or b < 0:
				raise ValueError('''the value of both inputs must be positive'''     )
		SCREAMING_SNAKE_CASE       :     Union[str, Any]				= str(bin(a_     )     )[2:]  # remove the leading "0b"
		SCREAMING_SNAKE_CASE       :     Optional[Any]				= str(bin(a_     )     )[2:]
		SCREAMING_SNAKE_CASE       :     int				= max(len(a_     )		,		len(a_     )     )
		return "0b" + "".join(
		    str(int('''1''' in (char_a, char_b)     )     )
		    for char_a, char_b in zip(a_binary.zfill(a_     )		,		b_binary.zfill(a_     )     )     )


if __name__ == "__main__":
					import doctest

					doctest.testmod()







"""simple docstring"""






from __future__ import annotations

from fractions import Fraction





def __A						(   a_ :							int		,		a_ :							int     )->							bool:




		'''simple docstring'''






		return (
		    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
		)





def __A						(   a_ :							int     )->							list[str]:




		'''simple docstring'''






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





def __A						(   a_ :							int = 2     )->							int:




		'''simple docstring'''






		SCREAMING_SNAKE_CASE       :     Optional[Any]				= 1.0
		for fraction in fraction_list(a_     ):
				SCREAMING_SNAKE_CASE       :     List[str]				= Fraction(a_     )
				result *= frac.denominator / frac.numerator
		return int(a_     )


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





