

'''simple docstring'''

from __future__ import annotations

from fractions import Fraction





def    A_  ( snake_case      ,       snake_case ):
 return (
     num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
 )





def    A_  ( snake_case ):
 SCREAMING_SNAKE_CASE:str						      =					[]
 SCREAMING_SNAKE_CASE:Optional[Any]						      =					11
 SCREAMING_SNAKE_CASE:Any						      =					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
  SCREAMING_SNAKE_CASE:Optional[Any]						      =					10
 return solutions





def    A_  ( snake_case = 2 ):
 SCREAMING_SNAKE_CASE:Dict						      =					1.0
 for fraction in fraction_list(__UpperCamelCase ):
  SCREAMING_SNAKE_CASE:Dict						      =					Fraction(__UpperCamelCase )
  result *= frac.denominator / frac.numerator
 return int(__UpperCamelCase )


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









'''simple docstring'''

def    A_  ( snake_case = 100 ):
  SCREAMING_SNAKE_CASE:Dict						      =					0
  SCREAMING_SNAKE_CASE:Optional[int]						      =					0
  for i in range(1      ,       n + 1 ):
    sum_of_squares += i**2
    sum_of_ints += i
  return sum_of_ints**2 - sum_of_squares


if __name__ == "__main__":
    print(f'''{solution() = }''')






