
'''simple docstring'''







from __future__ import annotations







def   lowerCAmelCase(  a__    :  int      ):







       '''simple docstring'''






       lowerCamelCase__				   =      [0] * max_one

       for i in range(0      , a__      ):
              lowerCamelCase__				   =      i

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

       return totients







def   lowerCAmelCase(  a__    :  int      , a__    :  int      ):







       '''simple docstring'''






       return sorted(str(a__      )      ) == sorted(str(a__      )      )







def   lowerCAmelCase(  a__    :  int = 1000_0000      ):







       '''simple docstring'''






       lowerCamelCase__				   =      1  # i
       lowerCamelCase__				   =      0  # φ(i)
       lowerCamelCase__				   =      get_totients(max_n + 1      )

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

              if i * min_denominator < min_numerator * t and has_same_digits(a__      , a__      ):
                     lowerCamelCase__				   =      i
                     lowerCamelCase__				   =      t

       return min_numerator


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



'''simple docstring'''







from ..utils import DummyObject, requires_backends







class 		snake_case_       (						metaclass=A__						):



   """simple docstring"""





   __lowerCAmelCase	:							List[str]								=['''torch''', '''librosa''']







   def __init__( self			,   *UpperCamelCase			,   **UpperCamelCase):
          requires_backends(self			,   ["torch", "librosa"])







   @classmethod
   def     __UpperCAmelCase      ( cls			,   *UpperCamelCase			,   **UpperCamelCase):
          requires_backends(cls			,   ["torch", "librosa"])







   @classmethod
   def     __UpperCAmelCase      ( cls			,   *UpperCamelCase			,   **UpperCamelCase):
          requires_backends(cls			,   ["torch", "librosa"])







class 		snake_case_       (						metaclass=A__						):



   """simple docstring"""





   __lowerCAmelCase	:							Union[str, Any]								=['''torch''', '''librosa''']







   def __init__( self			,   *UpperCamelCase			,   **UpperCamelCase):
          requires_backends(self			,   ["torch", "librosa"])







   @classmethod
   def     __UpperCAmelCase      ( cls			,   *UpperCamelCase			,   **UpperCamelCase):
          requires_backends(cls			,   ["torch", "librosa"])







   @classmethod
   def     __UpperCAmelCase      ( cls			,   *UpperCamelCase			,   **UpperCamelCase):
          requires_backends(cls			,   ["torch", "librosa"])

