


'''simple docstring'''






def lowerCamelCase__     (		__lowerCamelCase			:				Optional[Any]				):







   '''simple docstring'''




   return [
       {
           0: [1, 2],
           1: [0, 2],
           2: [0, 1, 3, 5],
           3: [2, 4],
           4: [3],
           5: [2, 6, 8],
           6: [5, 7],
           7: [6, 8],
           8: [5, 7],
       },
       {
           0: [6],
           1: [9],
           2: [4, 5],
           3: [4],
           4: [2, 3],
           5: [2],
           6: [0, 7],
           7: [6],
           8: [],
           9: [1],
       },
       {
           0: [4],
           1: [6],
           2: [],
           3: [5, 6, 7],
           4: [0, 6],
           5: [3, 8, 9],
           6: [1, 3, 4, 7],
           7: [3, 6, 8, 9],
           8: [5, 7],
           9: [5, 7],
       },
       {
           0: [1, 3],
           1: [0, 2, 4],
           2: [1, 3, 4],
           3: [0, 2, 4],
           4: [1, 2, 3],
       },
   ][index]





def lowerCamelCase__     (		__lowerCamelCase			:				dict[int, list[int]]				):







   '''simple docstring'''




   _UpperCAmelCase  :  int				       =0
   _UpperCAmelCase  :  Optional[Any]				       =len(__lowerCamelCase				)  # No of vertices in graph
   _UpperCAmelCase  :  Any				       =[0] * n
   _UpperCAmelCase  :  Tuple				       =[False] * n

   def dfs(__lowerCamelCase			:				Any			,       __lowerCamelCase			:				Dict			,       __lowerCamelCase			:				Tuple			,       __lowerCamelCase			:				Optional[Any]				):
      _UpperCAmelCase  :  List[Any]				       =True
      _UpperCAmelCase  :  Optional[Any]				       =id_
      id_ += 1
      for to in graph[at]:
         if to == parent:
            pass
         elif not visited[to]:
            dfs(__lowerCamelCase			,       __lowerCamelCase			,       __lowerCamelCase			,       id_				)
            _UpperCAmelCase  :  Optional[int]				       =min(low[at]			,       low[to]				)
            if id_ <= low[to]:
               bridges.append((at, to) if at < to else (to, at)				)
         else:
            # This edge is a back edge and cannot be a bridge
            _UpperCAmelCase  :  List[str]				       =min(low[at]			,       low[to]				)

   _UpperCAmelCase  :  list[tuple[int, int]]				       =[]
   for i in range(__lowerCamelCase				):
      if not visited[i]:
         dfs(__lowerCamelCase			,       -1			,       __lowerCamelCase			,       id_				)
   return bridges


if __name__ == "__main__":
 import doctest

 doctest.testmod()





'''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())

