

'''simple docstring'''

from typing import TYPE_CHECKING

from ...utils import _LazyModule


lowerCAmelCase_     =      {"tokenization_bert_japanese": ["BertJapaneseTokenizer", "CharacterTokenizer", "MecabTokenizer"]}


if TYPE_CHECKING:
						from .tokenization_bert_japanese import BertJapaneseTokenizer, CharacterTokenizer, MecabTokenizer

else:
						import sys

						lowerCAmelCase_     =      _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)












'''simple docstring'''






import math
from collections.abc import Generator





def    lowercase_   (		lowercase__    ) ->Generator[int, None, None]:
						_snake_case: 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					,	lowercase__    ):
																		if (i % j) == 0:
																								break
												else:
																		yield i





def    lowercase_   (		lowercase__    ) ->Generator[int, None, None]:
						_snake_case: 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)
												_snake_case: int	       =		int(math.sqrt(lowercase__    )    ) + 1
												for j in range(2					,	lowercase__    ):
																		if (i % j) == 0:
																								break
												else:
																		yield i





def    lowercase_   (		lowercase__    ) ->Generator[int, None, None]:
						_snake_case: 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):
												_snake_case: List[str]	       =		int(math.sqrt(lowercase__    )    ) + 1
												for j in range(3					,	lowercase__					,	2    ):
																		# As we removed the even numbers, we don't need them now
																		if (i % j) == 0:
																								break
												else:
																		yield i





def    lowercase_   (		) ->Optional[int]:
						from timeit import timeit

						_snake_case: Dict	       =		'from __main__ import slow_primes, primes, fast_primes'
						print(timeit('slow_primes(1_000_000_000_000)'					,	setup=lowercase__					,	number=100_0000    )    )
						print(timeit('primes(1_000_000_000_000)'					,	setup=lowercase__					,	number=100_0000    )    )
						print(timeit('fast_primes(1_000_000_000_000)'					,	setup=lowercase__					,	number=100_0000    )    )


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





