"""simple docstring"""







# limitations under the License.


from typing import Optional, Tuple, Union

import torch

from diffusers import DiffusionPipeline, ImagePipelineOutput

class 		UpperCamelCase      (   lowercase						):



				def __init__(self    :				Union[str, Any]     ,  _A    :				Optional[Any]     ,  _A    :				str)   ->     int:
					super().__init__()
					self.register_modules(unet=_A     ,  scheduler=_A)






				@torch.no_grad()
				def __call__(self    :				Tuple     ,  _A    :				int = 1     ,  _A    :				Optional[torch.Generator] = None     ,  _A    :				int = 50     ,  _A    :				Optional[str] = "pil"     ,  _A    :				bool = True     ,  **_A    :				Tuple     ,  )   ->     Union[ImagePipelineOutput, Tuple]:
					__snake_case      :							int						=			torch.randn(
					    (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)     ,  generator=_A     ,  )
					__snake_case      :							Any						=			image.to(self.device)

					# set step values
					self.scheduler.set_timesteps(_A)

					for t in self.progress_bar(self.scheduler.timesteps):
						# 1. predict noise model_output
						__snake_case      :							Tuple						=			self.unet(_A     ,  _A).sample

						# 2. predict previous mean of image x_t-1 and add variance depending on eta
						# eta corresponds to η in paper and should be between [0, 1]
						# do x_t -> x_t-1
						__snake_case      :							List[Any]						=			self.scheduler.step(_A     ,  _A     ,  _A).prev_sample

					__snake_case      :							List[str]						=			(image / 2 + 0.5).clamp(0     ,  1)
					__snake_case      :							List[str]						=			image.cpu().permute(0     ,  2     ,  3     ,  1).numpy()
					if output_type == "pil":
						__snake_case      :							List[Any]						=			self.numpy_to_pil(_A)

					if not return_dict:
						return (image,), "This is a local test"

					return ImagePipelineOutput(images=_A), "This is a local test"






"""simple docstring"""







from __future__ import annotations

import math
def   __UpperCAmelCase    (   UpperCAmelCase_   :    int  )							->      bool:

	'''simple docstring'''





	if 1 < number < 4:
		# 2 and 3 are primes
		return True
	elif number < 2 or number % 2 == 0 or number % 3 == 0:
		# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
		return False

	# All primes number are in format of 6k +/- 1
	for i in range(5      ,							int(math.sqrt(UpperCAmelCase_  ) + 1  )      ,							6  ):
		if number % i == 0 or number % (i + 2) == 0:
			return False
	return True


_a					:					Any=			[num for num in range(3, 100_001, 2) if not is_prime(num)]
def   __UpperCAmelCase    (   UpperCAmelCase_   :    int  )							->      list[int]:

	'''simple docstring'''





	if not isinstance(UpperCAmelCase_      ,							UpperCAmelCase_  ):
		raise ValueError('n must be an integer'  )
	if n <= 0:
		raise ValueError('n must be >= 0'  )

	__snake_case      :							int						=			[]
	for num in range(len(UpperCAmelCase_  )  ):
		__snake_case      :							List[str]						=			0
		while 2 * i * i <= odd_composites[num]:
			__snake_case      :							List[Any]						=			odd_composites[num] - 2 * i * i
			if is_prime(UpperCAmelCase_  ):
				break
			i += 1
		else:
			list_nums.append(odd_composites[num]  )
			if len(UpperCAmelCase_  ) == n:
				return list_nums

	return []
def   __UpperCAmelCase    (   )							->      int:

	'''simple docstring'''





	return compute_nums(1  )[0]


if __name__ == "__main__":
	print(f'''{solution() = }''')





