


'''simple docstring'''






from typing import List, Optional, Tuple, Union

import PIL
import torch
from torchvision import transforms

from diffusers.pipeline_utils import DiffusionPipeline, ImagePipelineOutput
from diffusers.schedulers import DDIMScheduler
from diffusers.utils import randn_tensor


__A	:	List[str]     =     transforms.Compose(
    [
        transforms.Resize((256, 256)),
        transforms.ToTensor(),
        transforms.Normalize([0.5], [0.5]),
    ]
)





def      UpperCAmelCase      (		lowerCamelCase_  :Optional[int] ):







		'''simple docstring'''
		if isinstance(lowerCamelCase_				,      torch.Tensor ):
				return image
		elif isinstance(lowerCamelCase_				,      PIL.Image.Image ):
				snake_case_		:							Optional[int]			       =						[image]

		snake_case_		:							Optional[Any]			       =						[trans(img.convert("""RGB""" ) ) for img in image]
		snake_case_		:							str			       =						torch.stack(lowerCamelCase_ )
		return image






class 						__UpperCamelCase	(						lowercase__							):





							def __init__(  self		:Union[str, Any]  ,_UpperCamelCase		:int  ,_UpperCamelCase		:Tuple			):
									super().__init__()

									# make sure scheduler can always be converted to DDIM
									snake_case_		:							Dict			       =						DDIMScheduler.from_config(scheduler.config			)

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





							def 		a__   (  self		:int  ,_UpperCamelCase		:List[str]			):
									if strength < 0 or strength > 1:
											raise ValueError(F'''The value of strength should in [0.0, 1.0] but is {strength}'''			)





							def 		a__   (  self		:Union[str, Any]  ,_UpperCamelCase		:List[str]  ,_UpperCamelCase		:Dict  ,_UpperCamelCase		:List[Any]			):
									# get the original timestep using init_timestep
									snake_case_		:							Tuple			       =						min(int(num_inference_steps * strength			)  ,_UpperCamelCase			)

									snake_case_		:							List[str]			       =						max(num_inference_steps - init_timestep  ,0			)
									snake_case_		:							List[str]			       =						self.scheduler.timesteps[t_start:]

									return timesteps, num_inference_steps - t_start





							def 		a__   (  self		:Any  ,_UpperCamelCase		:Union[str, Any]  ,_UpperCamelCase		:List[Any]  ,_UpperCamelCase		:List[Any]  ,_UpperCamelCase		:List[str]  ,_UpperCamelCase		:Optional[int]  ,_UpperCamelCase		:Union[str, Any]=None			):
									if not isinstance(_UpperCamelCase  ,(torch.Tensor, PIL.Image.Image, list)			):
											raise ValueError(
											    F'''`image` has to be of type `torch.Tensor`, `PIL.Image.Image` or list but is {type(_UpperCamelCase			)}'''			)

									snake_case_		:							Tuple			       =						image.to(device=_UpperCamelCase  ,dtype=_UpperCamelCase			)

									if isinstance(_UpperCamelCase  ,_UpperCamelCase			) and len(_UpperCamelCase			) != batch_size:
											raise ValueError(
											    F'''You have passed a list of generators of length {len(_UpperCamelCase			)}, but requested an effective batch'''
											    F''' size of {batch_size}. Make sure the batch size matches the length of the generators.'''			)

									snake_case_		:							Tuple			       =						init_latents.shape
									snake_case_		:							Union[str, Any]			       =						randn_tensor(_UpperCamelCase  ,generator=_UpperCamelCase  ,device=_UpperCamelCase  ,dtype=_UpperCamelCase			)

									# get latents
									print("""add noise to latents at timestep"""  ,_UpperCamelCase			)
									snake_case_		:							int			       =						self.scheduler.add_noise(_UpperCamelCase  ,_UpperCamelCase  ,_UpperCamelCase			)
									snake_case_		:							Dict			       =						init_latents

									return latents





							@torch.no_grad()
							def __call__(  self		:List[Any]  ,_UpperCamelCase		:Union[torch.FloatTensor, PIL.Image.Image] = None  ,_UpperCamelCase		:float = 0.8  ,_UpperCamelCase		:int = 1  ,_UpperCamelCase		:Optional[Union[torch.Generator, List[torch.Generator]]] = None  ,_UpperCamelCase		:float = 0.0  ,_UpperCamelCase		:int = 5_0  ,_UpperCamelCase		:Optional[bool] = None  ,_UpperCamelCase		:Optional[str] = "pil"  ,_UpperCamelCase		:bool = True  ,):
									self.check_inputs(_UpperCamelCase			)

									# 2. Preprocess image
									snake_case_		:							Any			       =						preprocess(_UpperCamelCase			)

									# 3. set timesteps
									self.scheduler.set_timesteps(_UpperCamelCase  ,device=self.device			)
									snake_case_       ,      snake_case_		:							Union[str, Any]			       =						self.get_timesteps(_UpperCamelCase  ,_UpperCamelCase  ,self.device			)
									snake_case_		:							int			       =						timesteps[:1].repeat(_UpperCamelCase			)

									# 4. Prepare latent variables
									snake_case_		:							Union[str, Any]			       =						self.prepare_latents(_UpperCamelCase  ,_UpperCamelCase  ,_UpperCamelCase  ,self.unet.dtype  ,self.device  ,_UpperCamelCase			)
									snake_case_		:							Optional[int]			       =						latents

									# 5. Denoising loop
									for t in self.progress_bar(_UpperCamelCase			):
											# 1. predict noise model_output
											snake_case_		:							Tuple			       =						self.unet(_UpperCamelCase  ,_UpperCamelCase			).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[str]			       =						self.scheduler.step(
											    _UpperCamelCase  ,_UpperCamelCase  ,_UpperCamelCase  ,eta=_UpperCamelCase  ,use_clipped_model_output=_UpperCamelCase  ,generator=_UpperCamelCase  ,).prev_sample

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

									if not return_dict:
											return (image, latent_timestep.item())

									return ImagePipelineOutput(images=_UpperCamelCase			)



'''simple docstring'''






from __future__ import annotations





def      UpperCAmelCase      (		lowerCamelCase_  :int ):







		'''simple docstring'''
		snake_case_		:							List[str]			       =						[True] * limit
		snake_case_		:							Union[str, Any]			       =						False
		snake_case_		:							List[str]			       =						False
		snake_case_		:							Any			       =						True

		for i in range(3				,      int(limit**0.5 + 1 )				,      2 ):
				snake_case_		:							Tuple			       =						i * 2
				while index < limit:
						snake_case_		:							Any			       =						False
						snake_case_		:							Optional[Any]			       =						index + i

		snake_case_		:							List[str]			       =						[2]

		for i in range(3				,      lowerCamelCase_				,      2 ):
				if is_prime[i]:
						primes.append(lowerCamelCase_ )

		return primes





def      UpperCAmelCase      (		lowerCamelCase_  :int = 1_00_00_00 ):







		'''simple docstring'''
		snake_case_		:							Optional[int]			       =						prime_sieve(lowerCamelCase_ )
		snake_case_		:							Optional[Any]			       =						0
		snake_case_		:							Optional[int]			       =						0

		for i in range(len(lowerCamelCase_ ) ):
				for j in range(i + length				,      len(lowerCamelCase_ ) ):
						snake_case_		:							Optional[int]			       =						sum(primes[i:j] )
						if sol >= ceiling:
								break

						if sol in primes:
								snake_case_		:							Optional[Any]			       =						j - i
								snake_case_		:							Tuple			       =						sol

		return largest


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