




from __future__ import annotations

from collections import Counter


def   A		(__A  :       int			)  -> list[int]:







     """simple docstring"""


     UpperCAmelCase_		=				[True] * n
     UpperCAmelCase_		=				False
     UpperCAmelCase_		=				False
     UpperCAmelCase_		=				True

     for i in range(3  ,							int(n**0.5 + 1			)  ,							2			):
          UpperCAmelCase_		=				i * 2
          while index < n:
               UpperCAmelCase_		=				False
               UpperCAmelCase_		=				index + i

     UpperCAmelCase_		=				[2]

     for i in range(3  ,							__A  ,							2			):
          if is_prime[i]:
               primes.append(__A			)

     return primes


def   A		(__A  :       int			)  -> list[list[int]]:







     """simple docstring"""


     UpperCAmelCase_		=				str(__A			)
     UpperCAmelCase_		=				[]
     UpperCAmelCase_		=				['''0''', '''1''', '''2''', '''3''', '''4''', '''5''', '''6''', '''7''', '''8''', '''9''']

     for duplicate in Counter(__A			) - Counter(set(__A			)			):
          UpperCAmelCase_		=				[int(number_str.replace(__A  ,							__A			)			) for digit in digits]
          replacements.append(__A			)

     return replacements


def   A		(__A  :       int = 8			)  -> int:







     """simple docstring"""


     UpperCAmelCase_		=				set()

     # Filter primes with less than 3 replaceable digits
     UpperCAmelCase_		=				{
         x for x in set(prime_sieve(1000000			)			) if len(str(__A			)			) - len(set(str(__A			)			)			) >= 3
     }

     for prime in primes:
          if prime in numbers_checked:
               continue

          UpperCAmelCase_		=				digit_replacements(__A			)

          for family in replacements:
               numbers_checked.update(__A			)
               UpperCAmelCase_		=				primes.intersection(__A			)

               if len(__A			) != family_length:
                    continue

               return min(__A			)

     return -1


if __name__ == "__main__":
    print(solution())












import math


def   A		(__A  :       int			)  -> float:







     """simple docstring"""


     UpperCAmelCase_		=				math.log(2  ,							10			) * number
     UpperCAmelCase_		=				round((log_number - int(__A			))  ,							15			)

     return difference


def   A		(__A  :       int = 678910			)  -> int:







     """simple docstring"""


     UpperCAmelCase_		=				90
     UpperCAmelCase_		=				0

     UpperCAmelCase_		=				math.log(1.23  ,							10			)
     UpperCAmelCase_		=				math.log(1.24  ,							10			)
     UpperCAmelCase_		=				0

     while position < number:
          UpperCAmelCase_		=				log_difference(__A			)

          if difference >= upper_limit:
               power_iterator += 93

          elif difference < lower_limit:
               power_iterator += 196

          else:
               UpperCAmelCase_		=				power_iterator
               power_iterator += 196
               position += 1

     return previous_power


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    print(f"{solution() = }")






