


'''simple docstring'''




from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


_lowerCAmelCase	:		int		  =						{
    'configuration_prophetnet': ['PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP', 'ProphetNetConfig'],
    'tokenization_prophetnet': ['ProphetNetTokenizer'],
}

try:
				if not is_torch_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				_lowerCAmelCase	:		int		  =						[
				    'PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST',
				    'ProphetNetDecoder',
				    'ProphetNetEncoder',
				    'ProphetNetForCausalLM',
				    'ProphetNetForConditionalGeneration',
				    'ProphetNetModel',
				    'ProphetNetPreTrainedModel',
				]


if TYPE_CHECKING:
				from .configuration_prophetnet import PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP, ProphetNetConfig
				from .tokenization_prophetnet import ProphetNetTokenizer

				try:
								if not is_torch_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_prophetnet import (
								    PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST,
								    ProphetNetDecoder,
								    ProphetNetEncoder,
								    ProphetNetForCausalLM,
								    ProphetNetForConditionalGeneration,
								    ProphetNetModel,
								    ProphetNetPreTrainedModel,
								)

else:
				import sys

				_lowerCAmelCase	:		int		  =						_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




'''simple docstring'''




import math
from collections.abc import Generator

def       __UpperCamelCase     (     _A     :					int					)     ->   Generator[int, None, None]:




	"""simple docstring"""





	lowerCAmelCase       :     Generator   				=			(i for i in range(1       , (max_n + 1)					))
	for i in (n for n in numbers if n > 1):
		for j in range(2       , _A					):
			if (i % j) == 0:
				break
		else:
			yield i

def       __UpperCamelCase     (     _A     :					int					)     ->   Generator[int, None, None]:




	"""simple docstring"""





	lowerCAmelCase       :     Generator   				=			(i for i in range(1       , (max_n + 1)					))
	for i in (n for n in numbers if n > 1):
		# only need to check for factors up to sqrt(i)
		lowerCAmelCase       :     List[str]   				=			int(math.sqrt(_A					)					) + 1
		for j in range(2       , _A					):
			if (i % j) == 0:
				break
		else:
			yield i

def       __UpperCamelCase     (     _A     :					int					)     ->   Generator[int, None, None]:




	"""simple docstring"""





	lowerCAmelCase       :     Generator   				=			(i for i in range(1       , (max_n + 1)       , 2					))
	# It's useless to test even numbers as they will not be prime
	if max_n > 2:
		yield 2  # Because 2 will not be tested, it's necessary to yield it now
	for i in (n for n in numbers if n > 1):
		lowerCAmelCase       :     int   				=			int(math.sqrt(_A					)					) + 1
		for j in range(3       , _A       , 2					):
			# As we removed the even numbers, we don't need them now
			if (i % j) == 0:
				break
		else:
			yield i

def       __UpperCamelCase     (     )     ->   Dict:




	"""simple docstring"""





	from timeit import timeit

	lowerCAmelCase       :     Tuple   				=			'from __main__ import slow_primes, primes, fast_primes'
	print(timeit('slow_primes(1_000_000_000_000)'       , setup=_A       , number=1_00_00_00					)					)
	print(timeit('primes(1_000_000_000_000)'       , setup=_A       , number=1_00_00_00					)					)
	print(timeit('fast_primes(1_000_000_000_000)'       , setup=_A       , number=1_00_00_00					)					)


if __name__ == "__main__":
				_lowerCAmelCase	:		Optional[Any]		  =						int(input('Calculate primes up to:\n>> ').strip())
				for ret in primes(number):
								print(ret)
				benchmark()
