



'''simple docstring'''







_UpperCamelCase  						=			float("""inf""")

class      lowerCamelCase__     :






	'''simple docstring'''

	def __init__(  self		:  List[Any]   ,		__A		:  Any					)     ->			str:




								'''simple docstring'''





								lowerCAmelCase__  =   [0] * n
								lowerCAmelCase__  =   [0] * n
								lowerCAmelCase__  =   [0] * n
								lowerCAmelCase__  =   [[] for _ in range(__A					)]




	def      lowercase__							(  self		:  Union[str, Any]   ,		__A		:  Optional[int]   ,		__A		:  Dict   ,		__A		:  Optional[Any]   ,		__A		:  Optional[int]=0					)     ->			Optional[Any]:




								'''simple docstring'''





								self.adj[a].append([b, len(self.adj[b]					), c, 0]					)
								self.adj[b].append([a, len(self.adj[a]					) - 1, rcap, 0]					)




	def      lowercase__							(  self		:  Tuple   ,		__A		:  Optional[int]   ,		__A		:  List[str]   ,		__A		:  Dict					)     ->			str:




								'''simple docstring'''





								if vertex == sink or not flow:
															return flow

								for i in range(self.ptr[vertex]   ,		len(self.adj[vertex]					)					):
															lowerCAmelCase__  =   self.adj[vertex][i]
															if self.lvl[e[0]] == self.lvl[vertex] + 1:
																						lowerCAmelCase__  =   self.depth_first_search(e[0]   ,		__A   ,		min(__A   ,		e[2] - e[3]					)					)
																						if p:
																													self.adj[vertex][i][3] += p
																													self.adj[e[0]][e[1]][3] -= p
																													return p
															lowerCAmelCase__  =   self.ptr[vertex] + 1
								return 0




	def      lowercase__							(  self		:  Any   ,		__A		:  Tuple   ,		__A		:  Any					)     ->			str:




								'''simple docstring'''





								lowerCAmelCase__  ,lowerCAmelCase__  =   0, source
								for l in range(31					):  # noqa: E741  l = 30 maybe faster for random data
															while True:
																						lowerCAmelCase__  ,lowerCAmelCase__  =   [0] * len(self.q					), [0] * len(self.q					)
																						lowerCAmelCase__  ,lowerCAmelCase__  ,lowerCAmelCase__  =   0, 1, 1
																						while qi < qe and not self.lvl[sink]:
																													lowerCAmelCase__  =   self.q[qi]
																													qi += 1
																													for e in self.adj[v]:
																																				if not self.lvl[e[0]] and (e[2] - e[3]) >> (30 - l):
																																											lowerCAmelCase__  =   e[0]
																																											qe += 1
																																											lowerCAmelCase__  =   self.lvl[v] + 1

																						lowerCAmelCase__  =   self.depth_first_search(__A   ,		__A   ,		__A					)
																						while p:
																													flow += p
																													lowerCAmelCase__  =   self.depth_first_search(__A   ,		__A   ,		__A					)

																						if not self.lvl[sink]:
																													break

								return flow
_UpperCamelCase  						=			Dinic(10)
_UpperCamelCase  						=			0
_UpperCamelCase  						=			9
for vertex in range(1, 5):
		graph.add_edge(source, vertex, 1)
for vertex in range(5, 9):
		graph.add_edge(vertex, sink, 1)
for vertex in range(1, 5):
		graph.add_edge(vertex, vertex + 4, 1)

# Now we can know that is the maximum flow(source -> sink)
print(graph.max_flow(source, sink))










'''simple docstring'''







from typing import Optional

import torch
from PIL import Image
from tqdm.auto import tqdm
from transformers import CLIPTextModel, CLIPTokenizer

from diffusers import AutoencoderKL, DDIMScheduler, DiffusionPipeline, UNetaDConditionModel
from diffusers.image_processor import VaeImageProcessor
from diffusers.utils import (
    deprecate,
)

class      lowerCamelCase__     (     _A				):






	'''simple docstring'''

	def __init__(  self		:  Optional[Any]   ,		__A		:  AutoencoderKL   ,		__A		:  CLIPTextModel   ,		__A		:  CLIPTokenizer   ,		__A		:  UNetaDConditionModel   ,		__A		:  DDIMScheduler   ,		__A		:  float = 0.9_3   ,		__A		:  bool = True   ,		)     ->			int:




								'''simple docstring'''





								lowerCAmelCase__  =   mixing_coeff
								lowerCAmelCase__  =   leapfrog_steps

								super().__init__()
								self.register_modules(
								    vae=__A   ,		text_encoder=__A   ,		tokenizer=__A   ,		unet=__A   ,		scheduler=__A   ,		)

								lowerCAmelCase__  =   2 ** (len(self.vae.config.block_out_channels					) - 1)
								lowerCAmelCase__  =   VaeImageProcessor(vae_scale_factor=self.vae_scale_factor					)




	def      lowercase__							(  self		:  Optional[int]   ,		__A		:  str   ,		__A		:  Optional[str] = None   ,		__A		:  bool = False					)     ->			List[str]:




								'''simple docstring'''





								lowerCAmelCase__  =   self.tokenizer(
								    __A   ,		padding="""max_length"""   ,		max_length=self.tokenizer.model_max_length   ,		truncation=__A   ,		return_tensors="""pt"""   ,		)

								lowerCAmelCase__  =   self.text_encoder(text_inputs.input_ids.to(self.device					)					).last_hidden_state

								lowerCAmelCase__  =   prompt_embeds.to(dtype=self.text_encoder.dtype   ,		device=self.device					)

								if do_classifier_free_guidance:
															lowerCAmelCase__  =   """""" if negative_prompt is None else negative_prompt

															lowerCAmelCase__  =   self.tokenizer(
															    __A   ,		padding="""max_length"""   ,		max_length=self.tokenizer.model_max_length   ,		truncation=__A   ,		return_tensors="""pt"""   ,		)

															lowerCAmelCase__  =   self.text_encoder(uncond_input.input_ids.to(self.device					)					).last_hidden_state

															lowerCAmelCase__  =   torch.cat([negative_prompt_embeds, prompt_embeds]					)

								return prompt_embeds




	def      lowercase__							(  self		:  Optional[Any]   ,		__A		:  torch.Tensor   ,		__A		:  torch.Tensor					)     ->			Tuple:




								'''simple docstring'''





								lowerCAmelCase__  =   self.mixing_coeff * x + (1 - self.mixing_coeff) * y
								lowerCAmelCase__  =   self.mixing_coeff * y + (1 - self.mixing_coeff) * x

								return [x, y]




	def      lowercase__							(  self		:  Dict   ,		__A		:  torch.Tensor   ,		__A		:  torch.Tensor					)     ->			Union[str, Any]:




								'''simple docstring'''





								lowerCAmelCase__  =   (y - (1 - self.mixing_coeff) * x) / self.mixing_coeff
								lowerCAmelCase__  =   (x - (1 - self.mixing_coeff) * y) / self.mixing_coeff

								return [x, y]




	def      lowercase__							(  self		:  List[str]   ,		__A		:  torch.Tensor					)     ->			Dict:




								'''simple docstring'''





								lowerCAmelCase__  =   int(__A					)

								lowerCAmelCase__  =   self.scheduler.alphas_cumprod[t] if t >= 0 else self.scheduler.final_alpha_cumprod

								return alpha_prod, 1 - alpha_prod




	def      lowercase__							(  self		:  List[Any]   ,		__A		:  torch.Tensor   ,		__A		:  torch.Tensor   ,		__A		:  torch.Tensor   ,		__A		:  torch.Tensor   ,		)     ->			int:




								'''simple docstring'''





								lowerCAmelCase__  =   timestep - self.scheduler.config.num_train_timesteps / self.scheduler.num_inference_steps

								lowerCAmelCase__  ,lowerCAmelCase__  =   self._get_alpha_and_beta(__A					)
								lowerCAmelCase__  ,lowerCAmelCase__  =   self._get_alpha_and_beta(__A					)

								lowerCAmelCase__  =   (alpha_prod_t_prev / alpha_prod_t) ** 0.5
								lowerCAmelCase__  =   -a_t * (beta_prod_t**0.5) + beta_prod_t_prev**0.5

								lowerCAmelCase__  =   (base - b_t * model_output) / a_t

								return model_input, next_model_input.to(base.dtype					)




	def      lowercase__							(  self		:  Tuple   ,		__A		:  torch.Tensor   ,		__A		:  torch.Tensor   ,		__A		:  torch.Tensor   ,		__A		:  torch.Tensor   ,		)     ->			List[str]:




								'''simple docstring'''





								lowerCAmelCase__  =   timestep - self.scheduler.config.num_train_timesteps / self.scheduler.num_inference_steps

								lowerCAmelCase__  ,lowerCAmelCase__  =   self._get_alpha_and_beta(__A					)
								lowerCAmelCase__  ,lowerCAmelCase__  =   self._get_alpha_and_beta(__A					)

								lowerCAmelCase__  =   (alpha_prod_t_prev / alpha_prod_t) ** 0.5
								lowerCAmelCase__  =   -a_t * (beta_prod_t**0.5) + beta_prod_t_prev**0.5
								lowerCAmelCase__  =   a_t * base + b_t * model_output

								return model_input, next_model_input.to(base.dtype					)




	@torch.no_grad()
	def      lowercase__							(  self		:  int   ,		__A		:  torch.Tensor					)     ->			Union[str, Any]:




								'''simple docstring'''





								lowerCAmelCase__  =   1 / self.vae.config.scaling_factor * latents
								lowerCAmelCase__  =   self.vae.decode(__A					).sample
								lowerCAmelCase__  =   (image / 2 + 0.5).clamp(0   ,		1					)
								return image




	@torch.no_grad()
	def      lowercase__							(  self		:  List[str]   ,		__A		:  Image.Image   ,		__A		:  torch.Tensor   ,		__A		:  torch.Tensor   ,		__A		:  float   ,		__A		:  Optional[torch.Generator] = None   ,		)     ->			str:




								'''simple docstring'''





								lowerCAmelCase__  =   guidance_scale > 1.0

								lowerCAmelCase__  =   image.to(device=self.device   ,		dtype=text_embeds.dtype					)
								lowerCAmelCase__  =   self.vae.encode(__A					).latent_dist.sample(__A					)

								lowerCAmelCase__  =   self.vae.config.scaling_factor * latent

								lowerCAmelCase__  =   [latent.clone(), latent.clone()]

								for i, t in tqdm(enumerate(__A					)   ,		total=len(__A					)					):
															lowerCAmelCase__  =   self.noise_mixing_layer(x=coupled_latents[0]   ,		y=coupled_latents[1]					)

															# j - model_input index, k - base index
															for j in range(2					):
																						lowerCAmelCase__  =   j ^ 1

																						if self.leapfrog_steps:
																													if i % 2 == 0:
																																				lowerCAmelCase__  ,lowerCAmelCase__  =   j, k

																						lowerCAmelCase__  =   coupled_latents[j]
																						lowerCAmelCase__  =   coupled_latents[k]

																						lowerCAmelCase__  =   torch.cat([model_input] * 2					) if do_classifier_free_guidance else model_input

																						lowerCAmelCase__  =   self.unet(__A   ,		__A   ,		encoder_hidden_states=__A					).sample

																						if do_classifier_free_guidance:
																													lowerCAmelCase__  ,lowerCAmelCase__  =   noise_pred.chunk(2					)
																													lowerCAmelCase__  =   noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)

																						lowerCAmelCase__  ,lowerCAmelCase__  =   self.noise_step(
																						    base=__A   ,		model_input=__A   ,		model_output=__A   ,		timestep=__A   ,		)

																						lowerCAmelCase__  =   model_input

								return coupled_latents




	@torch.no_grad()
	def __call__(  self		:  List[Any]   ,		__A		:  str   ,		__A		:  str   ,		__A		:  Image.Image   ,		__A		:  float = 3.0   ,		__A		:  int = 50   ,		__A		:  float = 0.8   ,		__A		:  Optional[str] = None   ,		__A		:  Optional[torch.Generator] = None   ,		__A		:  Optional[str] = "pil"   ,		)     ->			Any:




								'''simple docstring'''





								lowerCAmelCase__  =   guidance_scale > 1.0

								lowerCAmelCase__  =   self.image_processor.preprocess(__A					)

								lowerCAmelCase__  =   self._encode_prompt(__A   ,		__A   ,		__A					)
								lowerCAmelCase__  =   self._encode_prompt(__A   ,		__A   ,		__A					)

								self.scheduler.set_timesteps(__A   ,		self.device					)

								lowerCAmelCase__  =   num_inference_steps - int(num_inference_steps * strength					)
								lowerCAmelCase__  =   self.scheduler.timesteps[t_limit:]
								lowerCAmelCase__  =   fwd_timesteps.flip(0					)

								lowerCAmelCase__  =   self.prepare_latents(__A   ,		__A   ,		__A   ,		__A   ,		__A					)

								for i, t in tqdm(enumerate(__A					)   ,		total=len(__A					)					):
															# j - model_input index, k - base index
															for k in range(2					):
																						lowerCAmelCase__  =   k ^ 1

																						if self.leapfrog_steps:
																													if i % 2 == 1:
																																				lowerCAmelCase__  ,lowerCAmelCase__  =   j, k

																						lowerCAmelCase__  =   coupled_latents[j]
																						lowerCAmelCase__  =   coupled_latents[k]

																						lowerCAmelCase__  =   torch.cat([model_input] * 2					) if do_classifier_free_guidance else model_input

																						lowerCAmelCase__  =   self.unet(__A   ,		__A   ,		encoder_hidden_states=__A					).sample

																						if do_classifier_free_guidance:
																													lowerCAmelCase__  ,lowerCAmelCase__  =   noise_pred.chunk(2					)
																													lowerCAmelCase__  =   noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)

																						lowerCAmelCase__  ,lowerCAmelCase__  =   self.denoise_step(
																						    base=__A   ,		model_input=__A   ,		model_output=__A   ,		timestep=__A   ,		)

																						lowerCAmelCase__  =   model_input

															lowerCAmelCase__  =   self.denoise_mixing_layer(x=coupled_latents[0]   ,		y=coupled_latents[1]					)

								# either one is fine
								lowerCAmelCase__  =   coupled_latents[0]

								if output_type not in ["latent", "pt", "np", "pil"]:
															lowerCAmelCase__  =   (
															    f'''the output_type {output_type} is outdated. Please make sure to set it to one of these instead: '''
															    """`pil`, `np`, `pt`, `latent`"""
															)
															deprecate("""Unsupported output_type"""   ,		"""1.0.0"""   ,		__A   ,		standard_warn=__A					)
															lowerCAmelCase__  =   """np"""

								if output_type == "latent":
															lowerCAmelCase__  =   final_latent
								else:
															lowerCAmelCase__  =   self.decode_latents(__A					)
															lowerCAmelCase__  =   self.image_processor.postprocess(__A   ,		output_type=__A					)

								return image





