





import inspect
from typing import List, Optional, Tuple, Union

import numpy as np
import PIL
import torch
import torch.utils.checkpoint

from ...models import UNetaDModel, VQModel
from ...schedulers import (
    DDIMScheduler,
    DPMSolverMultistepScheduler,
    EulerAncestralDiscreteScheduler,
    EulerDiscreteScheduler,
    LMSDiscreteScheduler,
    PNDMScheduler,
)
from ...utils import PIL_INTERPOLATION, randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput






def 	lowerCamelCase_		(							_UpperCamelCase					)						->		Dict:






				"""simple docstring"""


				snake_case_     ,				snake_case_		:       Optional[Any]           =    image.size
				snake_case_     ,				snake_case_		:       int           =    (x - x % 32 for x in (w, h))  # resize to integer multiple of 32
				snake_case_		:       Union[str, Any]           =    image.resize((w, h)					,							resample=PIL_INTERPOLATION['''lanczos''']					)
				snake_case_		:       int           =    np.array(_UpperCamelCase					).astype(np.floataa					) / 255.0
				snake_case_		:       Optional[int]           =    image[None].transpose(0					,							3					,							1					,							2					)
				snake_case_		:       Tuple           =    torch.from_numpy(_UpperCamelCase					)
				return 2.0 * image - 1.0





class    __lowerCAmelCase			(     _a	):






			def __init__(self   ,				__magic_name__   ,				__magic_name__   ,				__magic_name__   ,				)	->  Any:


							'''simple docstring'''



							super().__init__()
							self.register_modules(vqvae=__magic_name__   ,				unet=__magic_name__   ,				scheduler=__magic_name__       )






			@torch.no_grad()
			def __call__(self   ,				__magic_name__ = None   ,				__magic_name__ = 1   ,				__magic_name__ = 100   ,				__magic_name__ = 0.0   ,				__magic_name__ = None   ,				__magic_name__ = "pil"   ,				__magic_name__ = True   ,				)	->  Union[Tuple, ImagePipelineOutput]:


							'''simple docstring'''



							if isinstance(__magic_name__   ,				PIL.Image.Image       ):
											snake_case_		:       Tuple           =    1
							elif isinstance(__magic_name__   ,				torch.Tensor       ):
											snake_case_		:       List[str]           =    image.shape[0]
							else:
											raise ValueError(F'''`image` has to be of type `PIL.Image.Image` or `torch.Tensor` but is {type(__magic_name__       )}'''       )

							if isinstance(__magic_name__   ,				PIL.Image.Image       ):
											snake_case_		:       Optional[int]           =    preprocess(__magic_name__       )

							snake_case_     ,				snake_case_		:       Optional[int]           =    image.shape[-2:]

							# in_channels should be 6: 3 for latents, 3 for low resolution image
							snake_case_		:       int           =    (batch_size, self.unet.config.in_channels // 2, height, width)
							snake_case_		:       Optional[Any]           =    next(self.unet.parameters()       ).dtype

							snake_case_		:       Tuple           =    randn_tensor(__magic_name__   ,				generator=__magic_name__   ,				device=self.device   ,				dtype=__magic_name__       )

							snake_case_		:       str           =    image.to(device=self.device   ,				dtype=__magic_name__       )

							# set timesteps and move to the correct device
							self.scheduler.set_timesteps(__magic_name__   ,				device=self.device       )
							snake_case_		:       int           =    self.scheduler.timesteps

							# scale the initial noise by the standard deviation required by the scheduler
							snake_case_		:       Tuple           =    latents * self.scheduler.init_noise_sigma

							# prepare extra kwargs for the scheduler step, since not all schedulers have the same signature.
							# eta (η) is only used with the DDIMScheduler, it will be ignored for other schedulers.
							# eta corresponds to η in DDIM paper: https://arxiv.org/abs/2010.02502
							# and should be between [0, 1]
							snake_case_		:       List[str]           =    '''eta''' in set(inspect.signature(self.scheduler.step       ).parameters.keys()       )
							snake_case_		:       Optional[Any]           =    {}
							if accepts_eta:
											snake_case_		:       int           =    eta

							for t in self.progress_bar(__magic_name__       ):
											# concat latents and low resolution image in the channel dimension.
											snake_case_		:       str           =    torch.cat([latents, image]   ,				dim=1       )
											snake_case_		:       Tuple           =    self.scheduler.scale_model_input(__magic_name__   ,				__magic_name__       )
											# predict the noise residual
											snake_case_		:       Optional[int]           =    self.unet(__magic_name__   ,				__magic_name__       ).sample
											# compute the previous noisy sample x_t -> x_t-1
											snake_case_		:       Dict           =    self.scheduler.step(__magic_name__   ,				__magic_name__   ,				__magic_name__   ,				**__magic_name__       ).prev_sample

							# decode the image latents with the VQVAE
							snake_case_		:       Union[str, Any]           =    self.vqvae.decode(__magic_name__       ).sample
							snake_case_		:       str           =    torch.clamp(__magic_name__   ,				-1.0   ,				1.0       )
							snake_case_		:       Union[str, Any]           =    image / 2 + 0.5
							snake_case_		:       Optional[int]           =    image.cpu().permute(0   ,				2   ,				3   ,				1       ).numpy()

							if output_type == "pil":
											snake_case_		:       Optional[Any]           =    self.numpy_to_pil(__magic_name__       )

							if not return_dict:
											return (image,)

							return ImagePipelineOutput(images=__magic_name__       )




"""simple docstring"""




from collections import defaultdict





def       a_ (	lowercase__ :int     ):
			__lowerCamelCase          =      1
			__lowerCamelCase          =      True
			for v in tree[start]:
						if v not in visited:
									ret += dfs(lowercase__     )
			if ret % 2 == 0:
						cuts.append(lowercase__     )
			return ret





def       a_ (	):
			dfs(1     )


if __name__ == "__main__":
					__magic_name__  , __magic_name__						: Tuple    =				1_0, 9
					__magic_name__						: Tuple    =				defaultdict(list)
					__magic_name__						: dict[int, bool]    =				{}
					__magic_name__						: list[int]    =				[]
					__magic_name__						: List[str]    =				0
					__magic_name__						: Tuple    =				[(2, 1), (3, 1), (4, 3), (5, 2), (6, 1), (7, 2), (8, 6), (9, 8), (1_0, 8)]
					for u, v in edges:
										tree[u].append(v)
										tree[v].append(u)
					even_tree()
					print(len(cuts) - 1)




