





from __future__ import annotations



def A_	(		A__				)  ->		list[int]:
       a__						:	int =				[True] * limit
       a__						:	Optional[Any] =				False
       a__						:	str =				False
       a__						:	int =				True

       for i in range(3		,      int(limit**0.5 + 1				)		,      2				):
              a__						:	Dict =				i * 2
              while index < limit:
                     a__						:	Union[str, Any] =				False
                     a__						:	List[str] =				index + i

       a__						:	Optional[int] =				[2]

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

       return primes



def A_	(		A__ = 100_0000				)  ->		int:
       a__						:	Any =				prime_sieve(A__				)
       a__						:	Optional[int] =				0
       a__						:	Any =				0

       for i in range(len(A__				)				):
              for j in range(i + length		,      len(A__				)				):
                     a__						:	List[str] =				sum(primes[i:j]				)
                     if sol >= ceiling:
                            break

                     if sol in primes:
                            a__						:	List[Any] =				j - i
                            a__						:	Dict =				sol

       return largest


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









from math import loga



def A_	(		A__				)  ->		int:
       if a < 0:
              raise ValueError('Input value must be a positive integer'				)
       elif isinstance(A__		,      A__				):
              raise TypeError('Input value must be a \'int\' type'				)
       return 0 if (a == 0) else int(loga(a & -a				)				)


if __name__ == "__main__":
    import doctest

    doctest.testmod()


