



import math
from collections.abc import Generator


def 						UpperCAmelCase__   (   UpperCAmelCase__			:int       ):






 '''simple docstring'''

 a							=		(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			,       UpperCAmelCase__       ):
   if (i % j) == 0:
    break
  else:
   yield i


def 						UpperCAmelCase__   (   UpperCAmelCase__			:int       ):






 '''simple docstring'''

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


def 						UpperCAmelCase__   (   UpperCAmelCase__			:int       ):






 '''simple docstring'''

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


def 						UpperCAmelCase__   (   ):






 '''simple docstring'''

 from timeit import timeit

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


if __name__ == "__main__":
     A_		:  Tuple										=  int(input('''Calculate primes up to:\n>> ''').strip())
     for ret in primes(number):
          print(ret)
     benchmark()


"""simple docstring"""







from ...utils import (
    OptionalDependencyNotAvailable,
    is_torch_available,
    is_transformers_available,
    is_transformers_version,
)


try:
						if not (is_transformers_available() and is_torch_available() and is_transformers_version(""">=""", """4.27.0""")):
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						from ...utils.dummy_torch_and_transformers_objects import (
						    AudioLDMPipeline,
						)
else:
						from .pipeline_audioldm import AudioLDMPipeline

