



import math
from collections.abc import Generator



def  _lowerCAmelCase     (_lowerCAmelCase):
					UpperCamelCase_			= (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 ,						_lowerCAmelCase):
															if (i % j) == 0:
																				break
										else:
															yield i



def  _lowerCAmelCase     (_lowerCAmelCase):
					UpperCamelCase_			= (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)
										UpperCamelCase_			= int(math.sqrt(_lowerCAmelCase)) + 1
										for j in range(2 ,						_lowerCAmelCase):
															if (i % j) == 0:
																				break
										else:
															yield i



def  _lowerCAmelCase     (_lowerCAmelCase):
					UpperCamelCase_			= (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):
										UpperCamelCase_			= int(math.sqrt(_lowerCAmelCase)) + 1
										for j in range(3 ,						_lowerCAmelCase ,						2):
															# As we removed the even numbers, we don't need them now
															if (i % j) == 0:
																				break
										else:
															yield i



def  _lowerCAmelCase     ():
					from timeit import timeit

					UpperCamelCase_			= "from __main__ import slow_primes, primes, fast_primes"
					print(timeit("slow_primes(1_000_000_000_000)" ,						setup=_lowerCAmelCase ,						number=1_00_00_00))
					print(timeit("primes(1_000_000_000_000)" ,						setup=_lowerCAmelCase ,						number=1_00_00_00))
					print(timeit("fast_primes(1_000_000_000_000)" ,						setup=_lowerCAmelCase ,						number=1_00_00_00))


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





from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available, is_tokenizers_available


UpperCAmelCase__			:   Optional[Any]      			=    {}

try:
					if not is_sentencepiece_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					UpperCAmelCase__			:   List[Any]      			=    ['MBart50Tokenizer']

try:
					if not is_tokenizers_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					UpperCAmelCase__			:   int      			=    ['MBart50TokenizerFast']


if TYPE_CHECKING:
					try:
										if not is_sentencepiece_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .tokenization_mbartaa import MBartaaTokenizer

					try:
										if not is_tokenizers_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .tokenization_mbartaa_fast import MBartaaTokenizerFast

else:
					import sys

					UpperCAmelCase__			:   str      			=    _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)
