


'''simple docstring'''
from __future__ import annotations

from collections.abc import Generator


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



					'''simple docstring'''






					UpperCamelCase__   :dict[int, int]												= {}
					UpperCamelCase__   :Tuple												= 2
					while True:
										UpperCamelCase__   :str												= factor_map.pop(__a ,					__a   )
										if factor:
															UpperCamelCase__   :List[str]												= factor + prime
															while x in factor_map:
																				x += factor
															UpperCamelCase__   :Optional[Any]												= factor
										else:
															UpperCamelCase__   :List[str]												= prime
															yield prime
										prime += 1


def 			a      (			__a = 1e10   )  ->	int:



					'''simple docstring'''






					UpperCamelCase__   :Union[str, Any]												= sieve()

					UpperCamelCase__   :str												= 1
					while True:
										UpperCamelCase__   :Optional[Any]												= next(__a   )
										if (2 * prime * n) > limit:
															return n
										# Ignore the next prime as the reminder will be 2.
										next(__a   )
										n += 2


if __name__ == "__main__":
		print(solution())



'''simple docstring'''
from ...utils import (
    OptionalDependencyNotAvailable,
    is_flax_available,
    is_torch_available,
    is_transformers_available,
)


try:
		if not (is_transformers_available() and is_torch_available()):
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		from ...utils.dummy_torch_and_transformers_objects import *  # noqa F403
else:
		from .multicontrolnet import MultiControlNetModel
		from .pipeline_controlnet import StableDiffusionControlNetPipeline
		from .pipeline_controlnet_imgaimg import StableDiffusionControlNetImgaImgPipeline
		from .pipeline_controlnet_inpaint import StableDiffusionControlNetInpaintPipeline


if is_transformers_available() and is_flax_available():
		from .pipeline_flax_controlnet import FlaxStableDiffusionControlNetPipeline