


'''simple docstring'''

import math
import sys

def 							__magic_name__(						lowerCamelCase):
						if number != int(lowerCamelCase):
												raise ValueError('''the value of input must be a natural number''')
						if number < 0:
												raise ValueError('''the value of input must not be a negative number''')
						if number == 0:
												return 1
						__lowerCAmelCase							       =				[-1] * (number + 1)
						__lowerCAmelCase							       =				0
						for i in range(1,				number + 1):
												__lowerCAmelCase							       =				sys.maxsize
												__lowerCAmelCase							       =				int(math.sqrt(lowerCamelCase))
												for j in range(1,				root + 1):
																		__lowerCAmelCase							       =				1 + answers[i - (j**2)]
																		__lowerCAmelCase							       =				min(lowerCamelCase,				lowerCamelCase)
												__lowerCAmelCase							       =				answer
						return answers[number]


if __name__ == "__main__":
	import doctest

	doctest.testmod()





'''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


_UpperCAmelCase				: Tuple							    =				transforms.Compose(
    [
        transforms.Resize((2_5_6, 2_5_6)),
        transforms.ToTensor(),
        transforms.Normalize([0.5], [0.5]),
    ]
)

def 							__magic_name__(						lowerCamelCase):
						if isinstance(lowerCamelCase,				torch.Tensor):
												return image
						elif isinstance(lowerCamelCase,				PIL.Image.Image):
												__lowerCAmelCase							       =				[image]

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




class       a__				( __A      ):







				"""simple docstring"""



				def __init__(self       ,			__lowercase       ,			__lowercase		):
										super().__init__()

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

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




				def 					_snake_case  (self       ,			__lowercase		):
										if strength < 0 or strength > 1:
																raise ValueError(F"""The value of strength should in [0.0, 1.0] but is {strength}"""		)




				def 					_snake_case  (self       ,			__lowercase       ,			__lowercase       ,			__lowercase		):
										# get the original timestep using init_timestep
										__lowerCAmelCase							       =				min(int(num_inference_steps * strength		)       ,			__lowercase		)

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

										return timesteps, num_inference_steps - t_start




				def 					_snake_case  (self       ,			__lowercase       ,			__lowercase       ,			__lowercase       ,			__lowercase       ,			__lowercase       ,			__lowercase=None		):
										if not isinstance(__lowercase       ,			(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(__lowercase		)}"""		)

										__lowerCAmelCase							       =				image.to(device=__lowercase       ,			dtype=__lowercase		)

										if isinstance(__lowercase       ,			__lowercase		) and len(__lowercase		) != batch_size:
																raise ValueError(
																    F"""You have passed a list of generators of length {len(__lowercase		)}, 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(__lowercase       ,			generator=__lowercase       ,			device=__lowercase       ,			dtype=__lowercase		)

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

										return latents




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

										# 2. Preprocess image
										__lowerCAmelCase							       =				preprocess(__lowercase		)

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

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

										# 5. Denoising loop
										for t in self.progress_bar(__lowercase		):
																# 1. predict noise model_output
																__lowerCAmelCase							       =				self.unet(__lowercase       ,			__lowercase		).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(
																    __lowercase       ,			__lowercase       ,			__lowercase       ,			eta=__lowercase       ,			use_clipped_model_output=__lowercase       ,			generator=__lowercase       ,			).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(__lowercase		)

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

										return ImagePipelineOutput(images=__lowercase		)

