





'''simple docstring'''






from typing import List, Optional, Tuple, Union

import torch

from ...models import UNetaDModel
from ...schedulers import PNDMScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput







class       lowerCamelCase       (    SCREAMING_SNAKE_CASE__	):
					_SCREAMING_SNAKE_CASE				 =     42
					_SCREAMING_SNAKE_CASE				 =     42


					def __init__(       self						:	Union[str, Any]							,  __snake_case						:	Union[str, Any]							,  __snake_case						:	Any							):





											'''simple docstring'''





											super().__init__()

											_snake_case: Dict	       =		PNDMScheduler.from_config(scheduler.config							)

											self.register_modules(unet=_UpperCAmelCase							,  scheduler=_UpperCAmelCase							)




					@torch.no_grad()
					def __call__(       self						:	Optional[Any]							,  __snake_case						:	Optional[Any] = 1							,  __snake_case						:	Dict = 50							,  __snake_case						:	Union[str, Any] = None							,  __snake_case						:	Dict = "pil"							,  __snake_case						:	str = True							,  **__snake_case						:	Any							,  ):





											'''simple docstring'''





											_snake_case: int	       =		randn_tensor(
											    (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)							,  generator=_UpperCAmelCase							,  device=self.device							,  )

											self.scheduler.set_timesteps(_UpperCAmelCase							)
											for t in self.progress_bar(self.scheduler.timesteps							):
																	_snake_case: Union[str, Any]	       =		self.unet(_UpperCAmelCase							,  _UpperCAmelCase							).sample

																	_snake_case: Optional[int]	       =		self.scheduler.step(_UpperCAmelCase							,  _UpperCAmelCase							,  _UpperCAmelCase							).prev_sample

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

											if not return_dict:
																	return (image,)

											return ImagePipelineOutput(images=_UpperCAmelCase							)











'''simple docstring'''






import itertools

def      __lowerCAmelCase   (       snake_case__		):
			return (
			    int("".join(combination[0:2]		)		) * int("".join(combination[2:5]		)		)
			    == int("".join(combination[5:9]		)		)
			) or (
			    int("".join(combination[0]		)		) * int("".join(combination[1:5]		)		)
			    == int("".join(combination[5:9]		)		)
			)

def      __lowerCAmelCase   (       ):
			return sum(
			    {
			        int("".join(pandigital[5:9]		)		)
			        for pandigital in itertools.permutations("123456789"		)
			        if is_combination_valid(snake_case__		)
			    }		)


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



