



"""simple docstring"""






from __future__ import annotations


def 			_lowercase				(  __snake_case	)						->   list[int]:
			__lowerCAmelCase      :  Union[str, Any]												=       [True] * limit
			__lowerCAmelCase      :  Tuple												=       False
			__lowerCAmelCase      :  Any												=       False
			__lowerCAmelCase      :  int												=       True

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

			__lowerCAmelCase      :  Union[str, Any]												=       [2]

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

			return primes


def 			_lowercase				(  __snake_case = 1_000_000	)						->   int:
			__lowerCAmelCase      :  int												=       prime_sieve(__snake_case	)
			__lowerCAmelCase      :  Union[str, Any]												=       0
			__lowerCAmelCase      :  Optional[Any]												=       0

			for i in range(len(__snake_case	)	):
						for j in range(i + length					,len(__snake_case	)	):
									__lowerCAmelCase      :  List[Any]												=       sum(primes[i:j]	)
									if sol >= ceiling:
												break

									if sol in primes:
												__lowerCAmelCase      :  str												=       j - i
												__lowerCAmelCase      :  Any												=       sol

			return largest


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




"""simple docstring"""






from ..utils import DummyObject, requires_backends



class 			A__   (  metaclass=__SCREAMING_SNAKE_CASE							):




	'''simple docstring'''





	SCREAMING_SNAKE_CASE          =	['torch', 'torchsde']

	def __init__(     self:		int       ,			*_SCREAMING_SNAKE_CASE:		Optional[Any]       ,			**_SCREAMING_SNAKE_CASE:		str)				->       Dict:

				"""simple docstring"""

				requires_backends(self       ,			["torch", "torchsde"])

	@classmethod
	def 							_SCREAMING_SNAKE_CASE   (     cls:		Optional[Any]       ,			*_SCREAMING_SNAKE_CASE:		Optional[int]       ,			**_SCREAMING_SNAKE_CASE:		Optional[int])				->       Optional[Any]:

				"""simple docstring"""

				requires_backends(cls       ,			["torch", "torchsde"])







	@classmethod
	def 							_SCREAMING_SNAKE_CASE   (     cls:		Dict       ,			*_SCREAMING_SNAKE_CASE:		List[Any]       ,			**_SCREAMING_SNAKE_CASE:		Any)				->       Optional[int]:

				"""simple docstring"""

				requires_backends(cls       ,			["torch", "torchsde"])