


from __future__ import annotations

from collections import Counter




def   snake_case_	(    snake_case	)    ->							List[str]:
       lowercase__:  List[Any]         =  [True] * n
       lowercase__:  int         =  False
       lowercase__:  Any         =  False
       lowercase__:  List[Any]         =  True

       for i in range(3     ,				int(n**0.5 + 1	)     ,				2	):
              lowercase__:  str         =  i * 2
              while index < n:
                     lowercase__:  Optional[int]         =  False
                     lowercase__:  Optional[int]         =  index + i

       lowercase__:  Any         =  [2]

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

       return primes




def   snake_case_	(    snake_case	)    ->							str:
       lowercase__:  Tuple         =  str(UpperCAmelCase__	)
       lowercase__:  List[str]         =  []
       lowercase__:  Optional[Any]         =  ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']

       for duplicate in Counter(UpperCAmelCase__	) - Counter(set(UpperCAmelCase__	)	):
              lowercase__:  List[str]         =  [int(number_str.replace(UpperCAmelCase__     ,				UpperCAmelCase__	)	) for digit in digits]
              replacements.append(UpperCAmelCase__	)

       return replacements




def   snake_case_	(    snake_case = 8	)    ->							str:
       lowercase__:  List[str]         =  set()

       # Filter primes with less than 3 replaceable digits
       lowercase__:  int         =  {
           x for x in set(prime_sieve(1_00_00_00	)	) if len(str(UpperCAmelCase__	)	) - len(set(str(UpperCAmelCase__	)	)	) >= 3
       }

       for prime in primes:
              if prime in numbers_checked:
                     continue

              lowercase__:  Dict         =  digit_replacements(UpperCAmelCase__	)

              for family in replacements:
                     numbers_checked.update(UpperCAmelCase__	)
                     lowercase__:  Dict         =  primes.intersection(UpperCAmelCase__	)

                     if len(UpperCAmelCase__	) != family_length:
                            continue

                     return min(UpperCAmelCase__	)

       return -1


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







from __future__ import annotations


def 						UpperCAmelCase__   (   UpperCAmelCase__			:float | int			,       UpperCAmelCase__			:float | int			,       UpperCAmelCase__			:float | int			,       ):






 '''simple docstring'''

 if not all((nth_term, start_term_a, common_ratio_r)       ):
  return []
 a							=		[]
 a							=		1
 a							=		common_ratio_r
 for _ in range(int(UpperCAmelCase__       )       ):
  if not series:
   series.append(UpperCAmelCase__       )
  else:
   power += 1
   series.append(float(start_term_a * multiple       )       )
   a							=		pow(float(UpperCAmelCase__       )			,       UpperCAmelCase__       )
 return series


if __name__ == "__main__":
     import doctest

     doctest.testmod()

     A_		:  Optional[Any]										=  float(input('''Enter the last number (n term) of the Geometric Series'''))
     A_		:  Optional[Any]										=  float(input('''Enter the starting term (a) of the Geometric Series'''))
     A_		:  Optional[int]										=  float(
         input('''Enter the common ratio between two terms (r) of the Geometric Series''')
     )
     print('''Formula of Geometric Series => a + ar + ar^2 ... +ar^n''')
     print(geometric_series(nth_term, start_term_a, common_ratio_r))

