
"""simple docstring"""




from __future__ import annotations

from fractions import Fraction


def     __magic_name__      ( __snake_case							:			List[Any]	,					__snake_case							:			Tuple    )					->							bool:
       return (
           num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
       )


def     __magic_name__      ( __snake_case							:			Optional[int]    )					->							list[str]:
       lowercase       :							Union[str, Any]									=				[]
       lowercase       :							Dict									=				11
       lowercase       :							List[Any]									=				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
              lowercase       :							str									=				10
       return solutions


def     __magic_name__      ( __snake_case							:			str = 2    )					->							int:
       lowercase       :							List[Any]									=				1.0
       for fraction in fraction_list(_lowerCamelCase    ):
              lowercase       :							List[Any]									=				Fraction(_lowerCamelCase    )
              result *= frac.denominator / frac.numerator
       return int(_lowerCamelCase    )


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









'''simple docstring'''






from __future__ import annotations







def 					_a						(       _lowerCamelCase    ,	_lowerCamelCase = None    ,	_lowerCamelCase = None ) ->				None:



			"""simple docstring"""


			if start is None:
						__snake_case					:      Optional[Any]							      =     0

			if end is None:
						__snake_case					:      Optional[Any]							      =     len(_lowerCamelCase ) - 1

			if start >= end:
						return

			__snake_case					:      Tuple							      =     (start + end) // 2

			slowsort(_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )
			slowsort(_lowerCamelCase    ,	mid + 1    ,	_lowerCamelCase )

			if sequence[end] < sequence[mid]:
						__snake_case      ,     __snake_case					:      str							      =     sequence[mid], sequence[end]

			slowsort(_lowerCamelCase    ,	_lowerCamelCase    ,	end - 1 )


if __name__ == "__main__":
	from doctest import testmod

	testmod()


