






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


__snake_case    :    Optional[Any]         =     transforms.Compose(
    [
        transforms.Resize((2_56, 2_56)),
        transforms.ToTensor(),
        transforms.Normalize([0.5], [0.5]),
    ]
)







def 	_UpperCamelCase       (    UpperCamelCase_       :					Union[str, Any]		)  ->   int:

						"""simple docstring"""



						if isinstance(__A    ,       torch.Tensor		):
												return image
						elif isinstance(__A    ,       PIL.Image.Image		):
												lowerCAmelCase__    						=						[image]

						lowerCAmelCase__    						=						[trans(img.convert('RGB'		)		) for img in image]
						lowerCAmelCase__    						=						torch.stack(__A		)
						return image


class     __SCREAMING_SNAKE_CASE					(   _snake_case):






						def __init__(	self     ,						_UpperCamelCase     ,						_UpperCamelCase   ):






												"""simple docstring"""
												super().__init__()

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

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






						def       UpperCamelCase__      (	self     ,						_UpperCamelCase   ):






												"""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     ,						_UpperCamelCase     ,						_UpperCamelCase     ,						_UpperCamelCase   ):






												"""simple docstring"""
												# get the original timestep using init_timestep
												lowerCAmelCase__    						=						min(int(num_inference_steps * strength   )     ,						lowerCAmelCase__   )

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

												return timesteps, num_inference_steps - t_start






						def       UpperCamelCase__      (	self     ,						_UpperCamelCase     ,						_UpperCamelCase     ,						_UpperCamelCase     ,						_UpperCamelCase     ,						_UpperCamelCase     ,						_UpperCamelCase=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__   )}"   )

												lowerCAmelCase__    						=						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."   )

												lowerCAmelCase__    						=						init_latents.shape
												lowerCAmelCase__    						=						randn_tensor(lowerCAmelCase__     ,						generator=lowerCAmelCase__     ,						device=lowerCAmelCase__     ,						dtype=lowerCAmelCase__   )

												# get latents
												print('add noise to latents at timestep'     ,						lowerCAmelCase__   )
												lowerCAmelCase__    						=						self.scheduler.add_noise(lowerCAmelCase__     ,						lowerCAmelCase__     ,						lowerCAmelCase__   )
												lowerCAmelCase__    						=						init_latents

												return latents







						@torch.no_grad()
						def __call__(	self     ,						_UpperCamelCase = None     ,						_UpperCamelCase = 0.8     ,						_UpperCamelCase = 1     ,						_UpperCamelCase = None     ,						_UpperCamelCase = 0.0     ,						_UpperCamelCase = 50     ,						_UpperCamelCase = None     ,						_UpperCamelCase = "pil"     ,						_UpperCamelCase = True     ,						):






												"""simple docstring"""
												self.check_inputs(lowerCAmelCase__   )

												# 2. Preprocess image
												lowerCAmelCase__    						=						preprocess(lowerCAmelCase__   )

												# 3. set timesteps
												self.scheduler.set_timesteps(lowerCAmelCase__     ,						device=self.device   )
												lowerCAmelCase__						,       lowerCAmelCase__    						=						self.get_timesteps(lowerCAmelCase__     ,						lowerCAmelCase__     ,						self.device   )
												lowerCAmelCase__    						=						timesteps[:1].repeat(lowerCAmelCase__   )

												# 4. Prepare latent variables
												lowerCAmelCase__    						=						self.prepare_latents(lowerCAmelCase__     ,						lowerCAmelCase__     ,						lowerCAmelCase__     ,						self.unet.dtype     ,						self.device     ,						lowerCAmelCase__   )
												lowerCAmelCase__    						=						latents

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

												lowerCAmelCase__    						=						(image / 2 + 0.5).clamp(0     ,						1   )
												lowerCAmelCase__    						=						image.cpu().permute(0     ,						2     ,						3     ,						1   ).numpy()
												if output_type == "pil":
																		lowerCAmelCase__    						=						self.numpy_to_pil(lowerCAmelCase__   )

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

												return ImagePipelineOutput(images=lowerCAmelCase__   )













from __future__ import annotations

from functools import lru_cache
from math import ceil

__snake_case    :    Union[str, Any]         =     1_00

__snake_case    :    Tuple         =     set(range(3, NUM_PRIMES, 2))
primes.add(2)
__snake_case    :    int

for prime in range(3, ceil(NUM_PRIMES**0.5), 2):
					if prime not in primes:
										continue
					primes.difference_update(set(range(prime * prime, NUM_PRIMES, prime)))







@lru_cache(maxsize=100		)
def 	_UpperCamelCase   (    UpperCamelCase_       :					int		)  ->   set[int]:

						"""simple docstring"""



						if number_to_partition < 0:
												return set()
						elif number_to_partition == 0:
												return {1}

						lowerCAmelCase__    						=						set()
						lowerCAmelCase__    						=						42
						lowerCAmelCase__    						=						42

						for prime in primes:
												if prime > number_to_partition:
																		continue
												for sub in partition(number_to_partition - prime		):
																		ret.add(sub * prime		)

						return ret







def 	_UpperCamelCase   (    UpperCamelCase_       :					int = 5000		)  ->   int | None:

						"""simple docstring"""



						for number_to_partition in range(1    ,       UpperCamelCase_		):
												if len(partition(UpperCamelCase_		)		) > number_unique_partitions:
																		return number_to_partition
						return None


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





