





'''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


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

def       A__(		__lowerCAmelCase ):
				if isinstance(__lowerCAmelCase	,			torch.Tensor ):
								return image
				elif isinstance(__lowerCAmelCase	,			PIL.Image.Image ):
								_snake_case :			str  						=   [image]

				_snake_case :			Dict  						=   [trans(img.convert('RGB' ) ) for img in image]
				_snake_case :			Optional[Any]  						=   torch.stack(__lowerCAmelCase )
				return image


class 			lowercase				(							a_     ):



						"""simple docstring"""

						def __init__(    self			:		Optional[int] ,				lowerCamelCase_			:		Any ,				lowerCamelCase_			:		List[str]					):





										'''simple docstring'''







										super().__init__()

										# make sure scheduler can always be converted to DDIM
										_snake_case :			List[str]  						=   DDIMScheduler.from_config(scheduler.config					)

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







						def 		__UpperCAmelCase       (    self			:		Dict ,				lowerCamelCase_			:		Optional[int]					):





										'''simple docstring'''







										if strength < 0 or strength > 1:
														raise ValueError(f'''The value of strength should in [0.0, 1.0] but is {strength}'''					)







						def 		__UpperCAmelCase       (    self			:		Any ,				lowerCamelCase_			:		Optional[Any] ,				lowerCamelCase_			:		Any ,				lowerCamelCase_			:		Any					):





										'''simple docstring'''







										_snake_case :			Optional[int]  						=   min(int(num_inference_steps * strength					) ,				lowerCamelCase_					)

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

										return timesteps, num_inference_steps - t_start







						def 		__UpperCAmelCase       (    self			:		int ,				lowerCamelCase_			:		Optional[Any] ,				lowerCamelCase_			:		Optional[Any] ,				lowerCamelCase_			:		Union[str, Any] ,				lowerCamelCase_			:		Optional[Any] ,				lowerCamelCase_			:		Any ,				lowerCamelCase_			:		int=None					):





										'''simple docstring'''







										if not isinstance(lowerCamelCase_ ,				(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(lowerCamelCase_					)}'''					)

										_snake_case :			Optional[int]  						=   image.to(device=lowerCamelCase_ ,				dtype=lowerCamelCase_					)

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

										_snake_case :			Union[str, Any]  						=   init_latents.shape
										_snake_case :			List[Any]  						=   randn_tensor(lowerCamelCase_ ,				generator=lowerCamelCase_ ,				device=lowerCamelCase_ ,				dtype=lowerCamelCase_					)

										# get latents
										print('add noise to latents at timestep' ,				lowerCamelCase_					)
										_snake_case :			Optional[Any]  						=   self.scheduler.add_noise(lowerCamelCase_ ,				lowerCamelCase_ ,				lowerCamelCase_					)
										_snake_case :			List[str]  						=   init_latents

										return latents







						@torch.no_grad()
						def __call__(    self			:		str ,				lowerCamelCase_			:		Union[torch.FloatTensor, PIL.Image.Image] = None ,				lowerCamelCase_			:		float = 0.8 ,				lowerCamelCase_			:		int = 1 ,				lowerCamelCase_			:		Optional[Union[torch.Generator, List[torch.Generator]]] = None ,				lowerCamelCase_			:		float = 0.0 ,				lowerCamelCase_			:		int = 50 ,				lowerCamelCase_			:		Optional[bool] = None ,				lowerCamelCase_			:		Optional[str] = "pil" ,				lowerCamelCase_			:		bool = True ,				):





										'''simple docstring'''







										self.check_inputs(lowerCamelCase_					)

										# 2. Preprocess image
										_snake_case :			Any  						=   preprocess(lowerCamelCase_					)

										# 3. set timesteps
										self.scheduler.set_timesteps(lowerCamelCase_ ,				device=self.device					)
										_snake_case :			Optional[int]  						=   self.get_timesteps(lowerCamelCase_ ,				lowerCamelCase_ ,				self.device					)
										_snake_case :			Optional[int]  						=   timesteps[:1].repeat(lowerCamelCase_					)

										# 4. Prepare latent variables
										_snake_case :			str  						=   self.prepare_latents(lowerCamelCase_ ,				lowerCamelCase_ ,				lowerCamelCase_ ,				self.unet.dtype ,				self.device ,				lowerCamelCase_					)
										_snake_case :			Any  						=   latents

										# 5. Denoising loop
										for t in self.progress_bar(lowerCamelCase_					):
														# 1. predict noise model_output
														_snake_case :			Any  						=   self.unet(lowerCamelCase_ ,				lowerCamelCase_					).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 :			str  						=   self.scheduler.step(
														    lowerCamelCase_ ,				lowerCamelCase_ ,				lowerCamelCase_ ,				eta=lowerCamelCase_ ,				use_clipped_model_output=lowerCamelCase_ ,				generator=lowerCamelCase_ ,				).prev_sample

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

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

										return ImagePipelineOutput(images=lowerCamelCase_					)













import itertools
import math

def       A__(		__lowerCAmelCase ):

				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(__lowerCAmelCase ) + 1 )	,			6 ):
								if number % i == 0 or number % (i + 2) == 0:
												return False
				return True

def       A__(		):
				_snake_case :			Optional[Any]  						=   2
				while True:
								if is_prime(__lowerCAmelCase ):
												yield num
								num += 1

def       A__(		__lowerCAmelCase = 1_00_01 ):
				return next(itertools.islice(prime_generator()	,			nth - 1	,			__lowerCAmelCase ) )


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






