


'''simple docstring'''






def lowerCamelCase__     (		__lowerCamelCase			:				int = 5_0				):







   '''simple docstring'''




   _UpperCAmelCase  :  str				       =[1] * (length + 1)

   for row_length in range(3			,       length + 1				):
      for block_length in range(3			,       row_length + 1				):
         for block_start in range(row_length - block_length				):
            ways_number[row_length] += ways_number[
                row_length - block_start - block_length - 1
            ]

         ways_number[row_length] += 1

   return ways_number[length]


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





'''simple docstring'''






from __future__ import annotations

from fractions import Fraction





def lowerCamelCase__     (		__lowerCamelCase			:				int			,       __lowerCamelCase			:				int				):







   '''simple docstring'''




   return (
       num != den and num % 1_0 == den // 1_0 and (num // 1_0) / (den % 1_0) == num / den
   )





def lowerCamelCase__     (		__lowerCamelCase			:				int				):







   '''simple docstring'''




   _UpperCAmelCase  :  Optional[int]				       =[]
   _UpperCAmelCase  :  Union[str, Any]				       =1_1
   _UpperCAmelCase  :  Union[str, Any]				       =int('1' + '0' * digit_len				)
   for num in range(__lowerCamelCase			,       __lowerCamelCase				):
      while den <= 9_9:
         if (num != den) and (num % 1_0 == den // 1_0) and (den % 1_0 != 0):
            if is_digit_cancelling(__lowerCamelCase			,       __lowerCamelCase				):
               solutions.append(f"{num}/{den}"				)
         den += 1
      num += 1
      _UpperCAmelCase  :  Optional[int]				       =1_0
   return solutions





def lowerCamelCase__     (		__lowerCamelCase			:				int = 2				):







   '''simple docstring'''




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


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

