



"""simple docstring"""




from __future__ import annotations


class 	a__		:


   def __init__(				self   :				Tuple,  lowerCAmelCase   :				int      )     ->							None:
         lowercase	:   Optional[Any]											= value
         lowercase	:   Node | None											= None
         lowercase	:   Node | None											= None




class 	a__		:
   _lowerCamelCase       				=					42


   def __init__(				self   :				int      )     ->							None:
         lowercase	:   Optional[Any]											= 0


   def 							lowercase					(				self   :				Any,  lowerCAmelCase   :				Node | None,  lowerCAmelCase   :				int      )     ->							None:
         if node is None:
               return

         if path_sum == self.target:
               self.paths += 1

         if node.left:
               self.depth_first_search(node.left,  path_sum + node.left.value      )
         if node.right:
               self.depth_first_search(node.right,  path_sum + node.right.value      )






   def 							lowercase					(				self   :				int,  lowerCAmelCase   :				Node | None,  lowerCAmelCase   :				int | None = None      )     ->							int:
         if node is None:
               return 0
         if target is not None:
               lowercase	:   List[Any]											= target

         self.depth_first_search(lowerCAmelCase,  node.value      )
         self.path_sum(node.left      )
         self.path_sum(node.right      )

         return self.paths


if __name__ == "__main__":
     import doctest

     doctest.testmod()





"""simple docstring"""




from __future__ import annotations


def 	lowercase__  (      _UpperCAmelCase					)  ->      list[int]:






      '''simple docstring'''


      lowercase	:   Optional[Any]											= [0] * max_one

      for i in range(0						,   _UpperCAmelCase					):
            lowercase	:   List[Any]											= i

      for i in range(2						,   _UpperCAmelCase					):
            if totients[i] == i:
                  for j in range(_UpperCAmelCase						,   _UpperCAmelCase						,   _UpperCAmelCase					):
                        totients[j] -= totients[j] // i

      return totients


def 	lowercase__  (      _UpperCAmelCase						,   _UpperCAmelCase					)  ->      bool:






      '''simple docstring'''


      return sorted(str(_UpperCAmelCase					)					) == sorted(str(_UpperCAmelCase					)					)


def 	lowercase__  (      _UpperCAmelCase = 10_00_00_00					)  ->      int:






      '''simple docstring'''


      lowercase	:   Union[str, Any]											= 1  # i
      lowercase	:   Any											= 0  # φ(i)
      lowercase	:   int											= get_totients(max_n + 1					)

      for i in range(2						,   max_n + 1					):
            lowercase	:   Any											= totients[i]

            if i * min_denominator < min_numerator * t and has_same_digits(_UpperCAmelCase						,   _UpperCAmelCase					):
                  lowercase	:   List[Any]											= i
                  lowercase	:   Optional[Any]											= t

      return min_numerator


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