


"""simple docstring"""


from __future__ import annotations

from fractions import Fraction




def   snake_case		(     UpperCamelCase__       :						int			,				UpperCamelCase__       :						int    )   ->      bool:
      return (
          num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
      )




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




def   snake_case		(     UpperCamelCase__       :						int = 2    )   ->      int:
      lowerCamelCase					:					Union[str, Any]        =	1.0
      for fraction in fraction_list(UpperCamelCase__    ):
            lowerCamelCase					:					Dict        =	Fraction(UpperCamelCase__    )
            result *= frac.denominator / frac.numerator
      return int(UpperCamelCase__    )


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








"""simple docstring"""


from __future__ import annotations

__lowerCamelCase      :int	    =		10




def   snake_case		(     UpperCamelCase__       :						list[int]    )   ->      list[int]:
      lowerCamelCase					:					int        =	1
      lowerCamelCase					:					Union[str, Any]        =	max(UpperCamelCase__    )
      while placement <= max_digit:
            # declare and initialize empty buckets
            lowerCamelCase					:					list[list]        =	[[] for _ in range(UpperCamelCase__    )]
            # split list_of_ints between the buckets
            for i in list_of_ints:
                  lowerCamelCase					:					Any        =	int((i / placement) % RADIX    )
                  buckets[tmp].append(UpperCamelCase__    )
            # put each buckets' contents into list_of_ints
            lowerCamelCase					:					Dict        =	0
            for b in range(UpperCamelCase__    ):
                  for i in buckets[b]:
                        lowerCamelCase					:					List[str]        =	i
                        a += 1
        # move to next
            placement *= RADIX
      return list_of_ints


if __name__ == "__main__":
    import doctest

    doctest.testmod()




