
import math
from collections.abc import Generator






def     lowerCamelCase__				(   a ) ->  Generator[int, None, None]:
   _A:    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     lowerCamelCase__				(   a ) ->  Generator[int, None, None]:
   _A:    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)
      _A:    Union[str, Any]						     =			int(math.sqrt(a ) ) + 1
      for j in range(2						,						a ):
         if (i % j) == 0:
            break
      else:
         yield i






def     lowerCamelCase__				(   a ) ->  Generator[int, None, None]:
   _A:    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):
      _A:    List[Any]						     =			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     lowerCamelCase__				(   ) ->  Union[str, Any]:
   from timeit import timeit

   _A:    List[str]						     =			'''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__":
   UpperCAmelCase__						:	Dict	     = 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_torch_available


UpperCAmelCase__						:	Any	     = {
    'configuration_decision_transformer': [
        'DECISION_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'DecisionTransformerConfig',
    ],
}

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase__						:	Optional[Any]	     = [
       'DECISION_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST',
       'DecisionTransformerGPT2Model',
       'DecisionTransformerGPT2PreTrainedModel',
       'DecisionTransformerModel',
       'DecisionTransformerPreTrainedModel',
   ]


if TYPE_CHECKING:
   from .configuration_decision_transformer import (
       DECISION_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
       DecisionTransformerConfig,
   )

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_decision_transformer import (
          DECISION_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
          DecisionTransformerGPTaModel,
          DecisionTransformerGPTaPreTrainedModel,
          DecisionTransformerModel,
          DecisionTransformerPreTrainedModel,
      )


else:
   import sys

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



