



'''simple docstring'''






from __future__ import annotations




def     snake_case_					(     lowerCAmelCase_		)->		list[int]:





       '''simple docstring'''


       _UpperCAmelCase  :						Optional[Any]			     = [True] * limit
       _UpperCAmelCase  :						Any			     = False
       _UpperCAmelCase  :						int			     = False
       _UpperCAmelCase  :						List[str]			     = True

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

       _UpperCAmelCase  :						int			     = [2]

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

       return primes




def     snake_case_					(     lowerCAmelCase_ = 1000000		)->		int:





       '''simple docstring'''


       _UpperCAmelCase  :						str			     = prime_sieve(lowerCAmelCase_		)
       _UpperCAmelCase  :						Dict			     = 0
       _UpperCAmelCase  :						Dict			     = 0

       for i in range(len(lowerCAmelCase_		)		):
              for j in range(i + length       ,   len(lowerCAmelCase_		)		):
                     _UpperCAmelCase  :						Optional[int]			     = sum(primes[i:j]		)
                     if sol >= ceiling:
                            break

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

       return largest


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








'''simple docstring'''






from numpy import exp, pi, sqrt




def     snake_case_					(     lowerCAmelCase_       ,   lowerCAmelCase_ = 0.0       ,   lowerCAmelCase_ = 1.0		)->		int:





       '''simple docstring'''


       return 1 / sqrt(2 * pi * sigma**2		) * exp(-((x - mu) ** 2) / (2 * sigma**2)		)


if __name__ == "__main__":
   import doctest

   doctest.testmod()



