

import math





def a(lowercase__	):





	'''simple docstring'''
	snake_case_      		= [True] * n
	snake_case_      		= False
	snake_case_      		= False
	snake_case_      		= True

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

	snake_case_      		= [2]

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

	return primes





def a(lowercase__ = 999966663333	):





	'''simple docstring'''
	snake_case_      		= math.floor(math.sqrt(lowercase__	)	) + 100
	snake_case_      		= prime_sieve(lowercase__	)

	snake_case_      		= 0
	snake_case_      		= 0
	snake_case_      		= primes[prime_index]

	while (last_prime**2) <= limit:
		snake_case_      		= primes[prime_index + 1]

		snake_case_      		= last_prime**2
		snake_case_      		= next_prime**2

		# Get numbers divisible by lps(current)
		snake_case_      		= lower_bound + last_prime
		while upper_bound > current <= limit:
			matches_sum += current
			current += last_prime

		# Reset the upper_bound
		while (upper_bound - next_prime) > limit:
			upper_bound -= next_prime

		# Add the numbers divisible by ups(current)
		snake_case_      		= upper_bound - next_prime
		while current > lower_bound:
			matches_sum += current
			current -= next_prime

		# Remove the numbers divisible by both ups and lps
		snake_case_      		= 0
		while upper_bound > current <= limit:
			if current <= lower_bound:
				# Increment the current number
				current += last_prime * next_prime
				continue

			if current > limit:
				break

			# Remove twice since it was added by both ups and lps
			matches_sum -= current * 2

			# Increment the current number
			current += last_prime * next_prime

		# Setup for next pair
		snake_case_      		= next_prime
		prime_index += 1

	return matches_sum


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



from ..utils import DummyObject, requires_backends


class SCREAMING_SNAKE_CASE  (		metaclass=__snake_case							):






			"""simple docstring"""




			__A						  =  ["""torch""", """transformers""", """onnx"""]


			def __init__(    self ,				*__UpperCamelCase ,				**__UpperCamelCase							):

				"""simple docstring"""


				requires_backends(self ,				['torch', 'transformers', 'onnx']							)


			@classmethod
			def 			__lowerCAmelCase (    cls ,				*__UpperCamelCase ,				**__UpperCamelCase							):

				"""simple docstring"""


				requires_backends(cls ,				['torch', 'transformers', 'onnx']							)







			@classmethod
			def 			__lowerCAmelCase (    cls ,				*__UpperCamelCase ,				**__UpperCamelCase							):

				"""simple docstring"""


				requires_backends(cls ,				['torch', 'transformers', 'onnx']							)







class SCREAMING_SNAKE_CASE  (		metaclass=__snake_case							):






			"""simple docstring"""




			__A						  =  ["""torch""", """transformers""", """onnx"""]


			def __init__(    self ,				*__UpperCamelCase ,				**__UpperCamelCase							):

				"""simple docstring"""


				requires_backends(self ,				['torch', 'transformers', 'onnx']							)


			@classmethod
			def 			__lowerCAmelCase (    cls ,				*__UpperCamelCase ,				**__UpperCamelCase							):

				"""simple docstring"""


				requires_backends(cls ,				['torch', 'transformers', 'onnx']							)







			@classmethod
			def 			__lowerCAmelCase (    cls ,				*__UpperCamelCase ,				**__UpperCamelCase							):

				"""simple docstring"""


				requires_backends(cls ,				['torch', 'transformers', 'onnx']							)







class SCREAMING_SNAKE_CASE  (		metaclass=__snake_case							):






			"""simple docstring"""




			__A						  =  ["""torch""", """transformers""", """onnx"""]


			def __init__(    self ,				*__UpperCamelCase ,				**__UpperCamelCase							):

				"""simple docstring"""


				requires_backends(self ,				['torch', 'transformers', 'onnx']							)


			@classmethod
			def 			__lowerCAmelCase (    cls ,				*__UpperCamelCase ,				**__UpperCamelCase							):

				"""simple docstring"""


				requires_backends(cls ,				['torch', 'transformers', 'onnx']							)







			@classmethod
			def 			__lowerCAmelCase (    cls ,				*__UpperCamelCase ,				**__UpperCamelCase							):

				"""simple docstring"""


				requires_backends(cls ,				['torch', 'transformers', 'onnx']							)







class SCREAMING_SNAKE_CASE  (		metaclass=__snake_case							):






			"""simple docstring"""




			__A						  =  ["""torch""", """transformers""", """onnx"""]


			def __init__(    self ,				*__UpperCamelCase ,				**__UpperCamelCase							):

				"""simple docstring"""


				requires_backends(self ,				['torch', 'transformers', 'onnx']							)


			@classmethod
			def 			__lowerCAmelCase (    cls ,				*__UpperCamelCase ,				**__UpperCamelCase							):

				"""simple docstring"""


				requires_backends(cls ,				['torch', 'transformers', 'onnx']							)







			@classmethod
			def 			__lowerCAmelCase (    cls ,				*__UpperCamelCase ,				**__UpperCamelCase							):

				"""simple docstring"""


				requires_backends(cls ,				['torch', 'transformers', 'onnx']							)







class SCREAMING_SNAKE_CASE  (		metaclass=__snake_case							):






			"""simple docstring"""




			__A						  =  ["""torch""", """transformers""", """onnx"""]


			def __init__(    self ,				*__UpperCamelCase ,				**__UpperCamelCase							):

				"""simple docstring"""


				requires_backends(self ,				['torch', 'transformers', 'onnx']							)


			@classmethod
			def 			__lowerCAmelCase (    cls ,				*__UpperCamelCase ,				**__UpperCamelCase							):

				"""simple docstring"""


				requires_backends(cls ,				['torch', 'transformers', 'onnx']							)







			@classmethod
			def 			__lowerCAmelCase (    cls ,				*__UpperCamelCase ,				**__UpperCamelCase							):

				"""simple docstring"""


				requires_backends(cls ,				['torch', 'transformers', 'onnx']							)







class SCREAMING_SNAKE_CASE  (		metaclass=__snake_case							):






			"""simple docstring"""




			__A						  =  ["""torch""", """transformers""", """onnx"""]


			def __init__(    self ,				*__UpperCamelCase ,				**__UpperCamelCase							):

				"""simple docstring"""


				requires_backends(self ,				['torch', 'transformers', 'onnx']							)


			@classmethod
			def 			__lowerCAmelCase (    cls ,				*__UpperCamelCase ,				**__UpperCamelCase							):

				"""simple docstring"""


				requires_backends(cls ,				['torch', 'transformers', 'onnx']							)







			@classmethod
			def 			__lowerCAmelCase (    cls ,				*__UpperCamelCase ,				**__UpperCamelCase							):

				"""simple docstring"""


				requires_backends(cls ,				['torch', 'transformers', 'onnx']							)
