





"""simple docstring"""






from collections import defaultdict

def      __A   (      a_    :int)		->		int:
				__a			:    Dict      							=	1
				__a			:    Any      							=	True
				for v in tree[start]:
								if v not in visited:
												ret += dfs(a_)
				if ret % 2 == 0:
								cuts.append(a_)
				return ret

def      __A   (      )		->		List[Any]:
				dfs(1)


if __name__ == "__main__":
		A      , A			      =	10, 9
		A			      =	defaultdict(list)
		A			      =	{}
		A			      =	[]
		A			      =	0
		A			      =	[(2, 1), (3, 1), (4, 3), (5, 2), (6, 1), (7, 2), (8, 6), (9, 8), (10, 8)]
		for u, v in edges:
				tree[u].append(v)
				tree[v].append(u)
		even_tree()
		print(len(cuts) - 1)



'''simple docstring'''
import inspect
from typing import Callable, List, Optional, Union

import torch
from transformers import CLIPImageProcessor, CLIPTextModel, CLIPTokenizer

from diffusers import DiffusionPipeline
from diffusers.models import AutoencoderKL, UNetaDConditionModel
from diffusers.pipelines.stable_diffusion import StableDiffusionPipelineOutput
from diffusers.pipelines.stable_diffusion.safety_checker import StableDiffusionSafetyChecker
from diffusers.schedulers import DDIMScheduler, LMSDiscreteScheduler, PNDMScheduler
from diffusers.utils import logging


lowerCAmelCase   : Any             =				logging.get_logger(__name__)  # pylint: disable=invalid-name




class        _UpperCamelCase	(    SCREAMING_SNAKE_CASE):


				'''simple docstring'''


				def __init__(     self							,      a_							,      a_							,      a_							,      a_							,      a_							,      a_							,      a_							,      )    ->  Union[str, Any]:
					super().__init__()
					self.register_modules(
					    vae=a_							,      text_encoder=a_							,      tokenizer=a_							,      unet=a_							,      scheduler=a_							,      safety_checker=a_							,      feature_extractor=a_							,      )

				def 	a__		(     self							,      a_ = "auto"							)    ->  Dict:
					if slice_size == "auto":
						# half the attention head size is usually a good trade-off between
						# speed and memory
						lowercase						:		Union[str, Any]   					=		self.unet.config.attention_head_dim // 2
					self.unet.set_attention_slice(a_							)

				def 	a__		(     self							)    ->  Dict:
					self.enable_attention_slicing(a_							)


				@torch.no_grad()
				def __call__(     self							,      a_							,      a_ = 5_1_2							,      a_ = 5_1_2							,      a_ = 5_0							,      a_ = 7.5							,      a_ = None							,      a_ = 1							,      a_ = 0.0							,      a_ = None							,      a_ = None							,      a_ = "pil"							,      a_ = True							,      a_ = None							,      a_ = 1							,      a_ = None							,      **a_							,      )    ->  Union[str, Any]:

					if isinstance(a_							,      a_							):
						lowercase						:		Tuple   					=		1
					elif isinstance(a_							,      a_							):
						lowercase						:		int   					=		len(a_							)
					else:
						raise ValueError(F'''`prompt` has to be of type `str` or `list` but is {type(a_							)}'''							)

					if height % 8 != 0 or width % 8 != 0:
						raise ValueError(F'''`height` and `width` have to be divisible by 8 but are {height} and {width}.'''							)

					if (callback_steps is None) or (
					    callback_steps is not None and (not isinstance(a_							,      a_							) or callback_steps <= 0)
					):
						raise ValueError(
						    F'''`callback_steps` has to be a positive integer but is {callback_steps} of type'''
						    F''' {type(a_							)}.'''							)

					# get prompt text embeddings
					lowercase						:		int   					=		self.tokenizer(
					    a_							,      padding="max_length"							,      max_length=self.tokenizer.model_max_length							,      return_tensors="pt"							,      )
					lowercase						:		List[Any]   					=		text_inputs.input_ids

					if text_input_ids.shape[-1] > self.tokenizer.model_max_length:
						lowercase						:		str   					=		self.tokenizer.batch_decode(text_input_ids[:, self.tokenizer.model_max_length :]							)
						logger.warning(
						    "The following part of your input was truncated because CLIP can only handle sequences up to"
						    F''' {self.tokenizer.model_max_length} tokens: {removed_text}'''							)
						lowercase						:		Dict   					=		text_input_ids[:, : self.tokenizer.model_max_length]

					if text_embeddings is None:
						lowercase						:		List[Any]   					=		self.text_encoder(text_input_ids.to(self.device							)							)[0]

					# duplicate text embeddings for each generation per prompt, using mps friendly method
					lowercase					,		lowercase					,		lowercase						:		List[Any]   					=		text_embeddings.shape
					lowercase						:		Tuple   					=		text_embeddings.repeat(1							,      a_							,      1							)
					lowercase						:		Optional[int]   					=		text_embeddings.view(bs_embed * num_images_per_prompt							,      a_							,      -1							)

					# here `guidance_scale` is defined analog to the guidance weight `w` of equation (2)
					# of the Imagen paper: https://arxiv.org/pdf/2205.11487.pdf . `guidance_scale = 1`
					# corresponds to doing no classifier free guidance.
					lowercase						:		str   					=		guidance_scale > 1.0
					# get unconditional embeddings for classifier free guidance
					if do_classifier_free_guidance:
						lowercase						:		List[str]
						if negative_prompt is None:
							lowercase						:		Optional[Any]   					=		[""]
						elif type(a_							) is not type(a_							):
							raise TypeError(
							    F'''`negative_prompt` should be the same type to `prompt`, but got {type(a_							)} !='''
							    F''' {type(a_							)}.'''							)
						elif isinstance(a_							,      a_							):
							lowercase						:		Tuple   					=		[negative_prompt]
						elif batch_size != len(a_							):
							raise ValueError(
							    F'''`negative_prompt`: {negative_prompt} has batch size {len(a_							)}, but `prompt`:'''
							    F''' {prompt} has batch size {batch_size}. Please make sure that passed `negative_prompt` matches'''
							    " the batch size of `prompt`."							)
						else:
							lowercase						:		Dict   					=		negative_prompt

						lowercase						:		Tuple   					=		text_input_ids.shape[-1]
						lowercase						:		Any   					=		self.tokenizer(
						    a_							,      padding="max_length"							,      max_length=a_							,      truncation=a_							,      return_tensors="pt"							,      )
						lowercase						:		Any   					=		self.text_encoder(uncond_input.input_ids.to(self.device							)							)[0]

						# duplicate unconditional embeddings for each generation per prompt, using mps friendly method
						lowercase						:		Union[str, Any]   					=		uncond_embeddings.shape[1]
						lowercase						:		Tuple   					=		uncond_embeddings.repeat(a_							,      a_							,      1							)
						lowercase						:		Optional[int]   					=		uncond_embeddings.view(batch_size * num_images_per_prompt							,      a_							,      -1							)

						# For classifier free guidance, we need to do two forward passes.
						# Here we concatenate the unconditional and text embeddings into a single batch
						# to avoid doing two forward passes
						lowercase						:		Optional[Any]   					=		torch.cat([uncond_embeddings, text_embeddings]							)

					# get the initial random noise unless the user supplied it

					# Unlike in other pipelines, latents need to be generated in the target device
					# for 1-to-1 results reproducibility with the CompVis implementation.
					# However this currently doesn't work in `mps`.
					lowercase						:		List[str]   					=		(batch_size * num_images_per_prompt, self.unet.config.in_channels, height // 8, width // 8)
					lowercase						:		Union[str, Any]   					=		(batch_size * num_images_per_prompt, self.unet.config.in_channels, 6_4, 6_4)
					lowercase						:		Union[str, Any]   					=		text_embeddings.dtype
					if latents is None:
						if self.device.type == "mps":
							# randn does not exist on mps
							lowercase						:		List[str]   					=		torch.randn(
							    a_							,      generator=a_							,      device="cpu"							,      dtype=a_							).to(self.device							)
							lowercase						:		Any   					=		torch.randn(a_							,      generator=a_							,      device="cpu"							,      dtype=a_							).to(
							    self.device							)
						else:
							lowercase						:		List[Any]   					=		torch.randn(
							    a_							,      generator=a_							,      device=self.device							,      dtype=a_							)
							lowercase						:		Optional[Any]   					=		torch.randn(a_							,      generator=a_							,      device=self.device							,      dtype=a_							)
					else:
						if latents_reference.shape != latents_shape:
							raise ValueError(F'''Unexpected latents shape, got {latents.shape}, expected {latents_shape}'''							)
						lowercase						:		Dict   					=		latents_reference.to(self.device							)
						lowercase						:		int   					=		latents.to(self.device							)

					# This is the key part of the pipeline where we
					# try to ensure that the generated images w/ the same seed
					# but different sizes actually result in similar images
					lowercase						:		int   					=		(latents_shape[3] - latents_shape_reference[3]) // 2
					lowercase						:		Union[str, Any]   					=		(latents_shape[2] - latents_shape_reference[2]) // 2
					lowercase						:		int   					=		latents_shape_reference[3] if dx >= 0 else latents_shape_reference[3] + 2 * dx
					lowercase						:		Dict   					=		latents_shape_reference[2] if dy >= 0 else latents_shape_reference[2] + 2 * dy
					lowercase						:		Optional[int]   					=		0 if dx < 0 else dx
					lowercase						:		Tuple   					=		0 if dy < 0 else dy
					lowercase						:		Optional[int]   					=		max(-dx							,      0							)
					lowercase						:		int   					=		max(-dy							,      0							)
					# import pdb
					# pdb.set_trace()
					lowercase						:		Union[str, Any]   					=		latents_reference[:, :, dy : dy + h, dx : dx + w]

					# set timesteps
					self.scheduler.set_timesteps(a_							)

					# Some schedulers like PNDM have timesteps as arrays
					# It's more optimized to move all timesteps to correct device beforehand
					lowercase						:		List[Any]   					=		self.scheduler.timesteps.to(self.device							)

					# scale the initial noise by the standard deviation required by the scheduler
					lowercase						:		List[str]   					=		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]
					lowercase						:		Optional[Any]   					=		"eta" in set(inspect.signature(self.scheduler.step							).parameters.keys()							)
					lowercase						:		List[str]   					=		{}
					if accepts_eta:
						lowercase						:		List[str]   					=		eta

					for i, t in enumerate(self.progress_bar(a_							)							):
						# expand the latents if we are doing classifier free guidance
						lowercase						:		Optional[int]   					=		torch.cat([latents] * 2							) if do_classifier_free_guidance else latents
						lowercase						:		int   					=		self.scheduler.scale_model_input(a_							,      a_							)

						# predict the noise residual
						lowercase						:		Dict   					=		self.unet(a_							,      a_							,      encoder_hidden_states=a_							).sample

						# perform guidance
						if do_classifier_free_guidance:
							lowercase					,		lowercase						:		Dict   					=		noise_pred.chunk(2							)
							lowercase						:		Optional[int]   					=		noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)

						# compute the previous noisy sample x_t -> x_t-1
						lowercase						:		int   					=		self.scheduler.step(a_							,      a_							,      a_							,      **a_							).prev_sample

						# call the callback, if provided
						if callback is not None and i % callback_steps == 0:
							callback(a_							,      a_							,      a_							)

					lowercase						:		List[Any]   					=		1 / 0.1_82_15 * latents
					lowercase						:		Tuple   					=		self.vae.decode(a_							).sample

					lowercase						:		Any   					=		(image / 2 + 0.5).clamp(0							,      1							)

					# we always cast to float32 as this does not cause significant overhead and is compatible with bfloat16
					lowercase						:		Any   					=		image.cpu().permute(0							,      2							,      3							,      1							).float().numpy()

					if self.safety_checker is not None:
						lowercase						:		Tuple   					=		self.feature_extractor(self.numpy_to_pil(a_							)							,      return_tensors="pt"							).to(
						    self.device							)
						lowercase					,		lowercase						:		Tuple   					=		self.safety_checker(
						    images=a_							,      clip_input=safety_checker_input.pixel_values.to(text_embeddings.dtype							)							)
					else:
						lowercase						:		Union[str, Any]   					=		None

					if output_type == "pil":
						lowercase						:		Union[str, Any]   					=		self.numpy_to_pil(a_							)

					if not return_dict:
						return (image, has_nsfw_concept)

					return StableDiffusionPipelineOutput(images=a_							,      nsfw_content_detected=a_							)


