




def       _a (		SCREAMING_SNAKE_CASE_				:							Tuple	):
					__lowerCAmelCase							  =			[True for i in range(n + 1	)]
					__lowerCAmelCase							  =			[i - 1 for i in range(n + 1	)]
					__lowerCAmelCase							  =			[]
					for i in range(2 , n + 1	):
										if is_prime[i]:
															primes.append(lowerCamelCase__	)
										for j in range(0 , len(lowerCamelCase__	)	):
															if i * primes[j] >= n:
																				break
															__lowerCAmelCase							  =			False

															if i % primes[j] == 0:
																				__lowerCAmelCase							  =			totients[i] * primes[j]
																				break

															__lowerCAmelCase							  =			totients[i] * (primes[j] - 1)

					return totients


if __name__ == "__main__":
					import doctest

					doctest.testmod()












from __future__ import annotations




def       _a   (							lowerCamelCase__				)  ->      list[int]:
 lowerCamelCase_							:    Any							=     [0] * max_one

 for i in range(0 ,			lowerCamelCase__				):
  lowerCamelCase_							:    Union[str, Any]							=     i

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

 return totients




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__				)  ->      bool:
 return sorted(str(lowerCamelCase__				)				) == sorted(str(lowerCamelCase__				)				)




def       _a   (							lowerCamelCase__ = 10_00_00_00				)  ->      int:
 lowerCamelCase_							:    Tuple							=     1  # i
 lowerCamelCase_							:    Union[str, Any]							=     0  # φ(i)
 lowerCamelCase_							:    List[Any]							=     get_totients(max_n + 1				)

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

  if i * min_denominator < min_numerator * t and has_same_digits(lowerCamelCase__ ,			lowerCamelCase__				):
   lowerCamelCase_							:    str							=     i
   lowerCamelCase_							:    List[Any]							=     t

 return min_numerator


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