





"""simple docstring"""


from __future__ import annotations





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

 '''simple docstring'''






 snake_case__     				=					[0] * max_one

 for i in range(0						,  _UpperCAmelCase						):
  snake_case__     				=					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 				a__      (	_UpperCAmelCase						,  _UpperCAmelCase						)     ->	bool:

 '''simple docstring'''






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





def 				a__      (	_UpperCAmelCase = 1_0_0_0_0_0_0_0						)     ->	int:

 '''simple docstring'''






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

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

  if i * min_denominator < min_numerator * t and has_same_digits(_UpperCAmelCase						,  _UpperCAmelCase						):
   snake_case__     				=					i
   snake_case__     				=					t

 return min_numerator


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






"""simple docstring"""




from __future__ import annotations

# Define the Gravitational Constant G and the function
_UpperCamelCase:					Tuple     				=	6.6_7_4_3e-1_1  # unit of G : m^3 * kg^-1 * s^-2


def 	lowercase__  (      _UpperCAmelCase						,   _UpperCAmelCase						,   _UpperCAmelCase						,   _UpperCAmelCase					)  ->      dict[str, float]:






      '''simple docstring'''


      lowercase	:   str											= mass_a * mass_a

      if (force, mass_a, mass_a, distance).count(0					) != 1:
            raise ValueError('One and only one argument must be 0'					)
      if force < 0:
            raise ValueError('Gravitational force can not be negative'					)
      if distance < 0:
            raise ValueError('Distance can not be negative'					)
      if mass_a < 0 or mass_a < 0:
            raise ValueError('Mass can not be negative'					)
      if force == 0:
            lowercase	:   str											= GRAVITATIONAL_CONSTANT * product_of_mass / (distance**2)
            return {"force": force}
      elif mass_a == 0:
            lowercase	:   Optional[int]											= (force) * (distance**2) / (GRAVITATIONAL_CONSTANT * mass_a)
            return {"mass_1": mass_a}
      elif mass_a == 0:
            lowercase	:   Optional[int]											= (force) * (distance**2) / (GRAVITATIONAL_CONSTANT * mass_a)
            return {"mass_2": mass_a}
      elif distance == 0:
            lowercase	:   List[Any]											= (GRAVITATIONAL_CONSTANT * product_of_mass / (force)) ** 0.5
            return {"distance": distance}
      raise ValueError('One and only one argument must be 0'					)


# Run doctest
if __name__ == "__main__":
     import doctest

     doctest.testmod()
