from __future__ import annotations

from fractions import Fraction







def      _a					(   lowercase__	:      int  ,	lowercase__	:      int			):







     '''simple docstring'''


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







def      _a					(   lowercase__	:      int			):







     '''simple docstring'''


     SCREAMING_SNAKE_CASE__					:					Dict      =		[]
     SCREAMING_SNAKE_CASE__					:					Dict      =		11
     SCREAMING_SNAKE_CASE__					:					Optional[int]      =		int('1' + '0' * digit_len			)
     for num in range(lowercase__  ,	lowercase__			):
          while den <= 99:
               if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
                    if is_digit_cancelling(lowercase__  ,	lowercase__			):
                         solutions.append(f'''{num}/{den}'''			)
               den += 1
          num += 1
          SCREAMING_SNAKE_CASE__					:					Tuple      =		10
     return solutions







def      _a					(   lowercase__	:      int = 2			):







     '''simple docstring'''


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


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





'''simple docstring'''




import random







def 						lowerCAmelCase_							(  snake_case__						,							snake_case__		):




    '''simple docstring'''



    A,    A,    A			:  Any   =		[], [], []
    for element in data:
        if element < pivot:
            less.append(snake_case__		)
        elif element > pivot:
            greater.append(snake_case__		)
        else:
            equal.append(snake_case__		)
    return less, equal, greater







def 						lowerCAmelCase_							(  snake_case__						,							snake_case__		):




    '''simple docstring'''



    if index >= len(snake_case__		) or index < 0:
        return None

    A			:  List[Any]   =		items[random.randint(0						,							len(snake_case__		) - 1		)]
    A			:  Optional[int]   =		0
    A,    A,    A			:  Dict   =		_partition(snake_case__						,							snake_case__		)
    A			:  int   =		len(snake_case__		)
    A			:  List[Any]   =		len(snake_case__		)

    # index is the pivot
    if m <= index < m + count:
        return pivot
    # must be in smaller
    elif m > index:
        return quick_select(snake_case__						,							snake_case__		)
    # must be in larger
    else:
        return quick_select(snake_case__						,							index - (m + count)		)




