


'''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 _snake_case (			a__ ):
							"""simple docstring"""





							def __init__( self      ,					__A      ,					__A      ,					__A      ,					__A      ,					__A      ,					__A = 0.93      ,					__A = True      ,					)  ->Optional[Any]:



											"""simple docstring"""







											__lowerCamelCase		:   List[Any]           =       mixing_coeff
											__lowerCamelCase		:   Tuple           =       leapfrog_steps

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

											__lowerCamelCase		:   str           =       2 ** (len(self.vae.config.block_out_channels						) - 1)
											__lowerCamelCase		:   Tuple           =       VaeImageProcessor(vae_scale_factor=self.vae_scale_factor						)







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A      ,					__A = None      ,					__A = False						)  ->Optional[Any]:



											"""simple docstring"""







											__lowerCamelCase		:   Any           =       self.tokenizer(
											    __A      ,					padding="max_length"      ,					max_length=self.tokenizer.model_max_length      ,					truncation=__A      ,					return_tensors="pt"      ,					)

											__lowerCamelCase		:   Tuple           =       self.text_encoder(text_inputs.input_ids.to(self.device						)						).last_hidden_state

											__lowerCamelCase		:   Tuple           =       prompt_embeds.to(dtype=self.text_encoder.dtype      ,					device=self.device						)

											if do_classifier_free_guidance:
															__lowerCamelCase		:   str           =       "" if negative_prompt is None else negative_prompt

															__lowerCamelCase		:   List[Any]           =       self.tokenizer(
															    __A      ,					padding="max_length"      ,					max_length=self.tokenizer.model_max_length      ,					truncation=__A      ,					return_tensors="pt"      ,					)

															__lowerCamelCase		:   Union[str, Any]           =       self.text_encoder(uncond_input.input_ids.to(self.device						)						).last_hidden_state

															__lowerCamelCase		:   Union[str, Any]           =       torch.cat([negative_prompt_embeds, prompt_embeds]						)

											return prompt_embeds







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A      ,					__A						)  ->Tuple:



											"""simple docstring"""







											__lowerCamelCase		:   List[str]           =       self.mixing_coeff * x + (1 - self.mixing_coeff) * y
											__lowerCamelCase		:   Optional[Any]           =       self.mixing_coeff * y + (1 - self.mixing_coeff) * x

											return [x, y]







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A      ,					__A						)  ->Optional[int]:



											"""simple docstring"""







											__lowerCamelCase		:   int           =       (y - (1 - self.mixing_coeff) * x) / self.mixing_coeff
											__lowerCamelCase		:   Dict           =       (x - (1 - self.mixing_coeff) * y) / self.mixing_coeff

											return [x, y]







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A						)  ->str:



											"""simple docstring"""







											__lowerCamelCase		:   Union[str, Any]           =       int(__A						)

											__lowerCamelCase		:   str           =       self.scheduler.alphas_cumprod[t] if t >= 0 else self.scheduler.final_alpha_cumprod

											return alpha_prod, 1 - alpha_prod







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A      ,					__A      ,					__A      ,					__A      ,					)  ->int:



											"""simple docstring"""







											__lowerCamelCase		:   List[Any]           =       timestep - self.scheduler.config.num_train_timesteps / self.scheduler.num_inference_steps

											__lowerCamelCase    ,       __lowerCamelCase		:   List[str]           =       self._get_alpha_and_beta(__A						)
											__lowerCamelCase    ,       __lowerCamelCase		:   List[str]           =       self._get_alpha_and_beta(__A						)

											__lowerCamelCase		:   Union[str, Any]           =       (alpha_prod_t_prev / alpha_prod_t) ** 0.5
											__lowerCamelCase		:   Tuple           =       -a_t * (beta_prod_t**0.5) + beta_prod_t_prev**0.5

											__lowerCamelCase		:   List[str]           =       (base - b_t * model_output) / a_t

											return model_input, next_model_input.to(base.dtype						)







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A      ,					__A      ,					__A      ,					__A      ,					)  ->Tuple:



											"""simple docstring"""







											__lowerCamelCase		:   Any           =       timestep - self.scheduler.config.num_train_timesteps / self.scheduler.num_inference_steps

											__lowerCamelCase    ,       __lowerCamelCase		:   int           =       self._get_alpha_and_beta(__A						)
											__lowerCamelCase    ,       __lowerCamelCase		:   int           =       self._get_alpha_and_beta(__A						)

											__lowerCamelCase		:   List[Any]           =       (alpha_prod_t_prev / alpha_prod_t) ** 0.5
											__lowerCamelCase		:   str           =       -a_t * (beta_prod_t**0.5) + beta_prod_t_prev**0.5
											__lowerCamelCase		:   int           =       a_t * base + b_t * model_output

											return model_input, next_model_input.to(base.dtype						)







							@torch.no_grad()
							def 		__SCREAMING_SNAKE_CASE( self      ,					__A						)  ->Dict:



											"""simple docstring"""







											__lowerCamelCase		:   Optional[Any]           =       1 / self.vae.config.scaling_factor * latents
											__lowerCamelCase		:   Optional[int]           =       self.vae.decode(__A						).sample
											__lowerCamelCase		:   Optional[Any]           =       (image / 2 + 0.5).clamp(0      ,					1						)
											return image







							@torch.no_grad()
							def 		__SCREAMING_SNAKE_CASE( self      ,					__A      ,					__A      ,					__A      ,					__A      ,					__A = None      ,					)  ->str:



											"""simple docstring"""







											__lowerCamelCase		:   Optional[int]           =       guidance_scale > 1.0

											__lowerCamelCase		:   int           =       image.to(device=self.device      ,					dtype=text_embeds.dtype						)
											__lowerCamelCase		:   Optional[Any]           =       self.vae.encode(__A						).latent_dist.sample(__A						)

											__lowerCamelCase		:   Any           =       self.vae.config.scaling_factor * latent

											__lowerCamelCase		:   Dict           =       [latent.clone(), latent.clone()]

											for i, t in tqdm(enumerate(__A						)      ,					total=len(__A						)						):
															__lowerCamelCase		:   str           =       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		:   Optional[Any]           =       j ^ 1

																			if self.leapfrog_steps:
																							if i % 2 == 0:
																											__lowerCamelCase    ,       __lowerCamelCase		:   Union[str, Any]           =       j, k

																			__lowerCamelCase		:   Optional[Any]           =       coupled_latents[j]
																			__lowerCamelCase		:   Any           =       coupled_latents[k]

																			__lowerCamelCase		:   List[str]           =       torch.cat([model_input] * 2						) if do_classifier_free_guidance else model_input

																			__lowerCamelCase		:   str           =       self.unet(__A      ,					__A      ,					encoder_hidden_states=__A						).sample

																			if do_classifier_free_guidance:
																							__lowerCamelCase    ,       __lowerCamelCase		:   Union[str, Any]           =       noise_pred.chunk(2						)
																							__lowerCamelCase		:   Tuple           =       noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)

																			__lowerCamelCase    ,       __lowerCamelCase		:   Tuple           =       self.noise_step(
																			    base=__A      ,					model_input=__A      ,					model_output=__A      ,					timestep=__A      ,					)

																			__lowerCamelCase		:   Tuple           =       model_input

											return coupled_latents







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



											"""simple docstring"""







											__lowerCamelCase		:   Union[str, Any]           =       guidance_scale > 1.0

											__lowerCamelCase		:   int           =       self.image_processor.preprocess(__A						)

											__lowerCamelCase		:   Union[str, Any]           =       self._encode_prompt(__A      ,					__A      ,					__A						)
											__lowerCamelCase		:   List[str]           =       self._encode_prompt(__A      ,					__A      ,					__A						)

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

											__lowerCamelCase		:   Tuple           =       num_inference_steps - int(num_inference_steps * strength						)
											__lowerCamelCase		:   List[Any]           =       self.scheduler.timesteps[t_limit:]
											__lowerCamelCase		:   Union[str, Any]           =       fwd_timesteps.flip(0						)

											__lowerCamelCase		:   Optional[Any]           =       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		:   int           =       k ^ 1

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

																			__lowerCamelCase		:   Optional[Any]           =       coupled_latents[j]
																			__lowerCamelCase		:   Tuple           =       coupled_latents[k]

																			__lowerCamelCase		:   Dict           =       torch.cat([model_input] * 2						) if do_classifier_free_guidance else model_input

																			__lowerCamelCase		:   Dict           =       self.unet(__A      ,					__A      ,					encoder_hidden_states=__A						).sample

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

																			__lowerCamelCase    ,       __lowerCamelCase		:   Dict           =       self.denoise_step(
																			    base=__A      ,					model_input=__A      ,					model_output=__A      ,					timestep=__A      ,					)

																			__lowerCamelCase		:   Any           =       model_input

															__lowerCamelCase		:   Union[str, Any]           =       self.denoise_mixing_layer(x=coupled_latents[0]      ,					y=coupled_latents[1]						)

											# either one is fine
											__lowerCamelCase		:   List[str]           =       coupled_latents[0]

											if output_type not in ["latent", "pt", "np", "pil"]:
															__lowerCamelCase		:   Tuple           =       (
															    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		:   Union[str, Any]           =       "np"

											if output_type == "latent":
															__lowerCamelCase		:   Optional[int]           =       final_latent
											else:
															__lowerCamelCase		:   List[str]           =       self.decode_latents(__A						)
															__lowerCamelCase		:   List[Any]           =       self.image_processor.postprocess(__A      ,					output_type=__A						)

											return image









'''simple docstring'''




from collections import deque





def 				a_							(    lowercase     )      ->Tuple:






				'''simple docstring'''

				return input(lowercase     ).strip().split(" "     )





def 				a_							(    lowercase				,    lowercase     )      ->dict[int, list[int]]:






				'''simple docstring'''

				__lowerCamelCase		:   dict[int, list[int]]           =       {}
				for i in range(lowercase     ):
								__lowerCamelCase		:   int           =       []

				for e in range(lowercase     ):
								__lowerCamelCase    ,       __lowerCamelCase		:   int           =       (int(lowercase     ) for i in _input(F'Edge {e + 1}: <node1> <node2> '     ))
								graph[x].append(lowercase     )
				return graph





def 				a_							(    lowercase				,    lowercase     )      ->dict[int, list[int]]:






				'''simple docstring'''

				__lowerCamelCase		:   dict[int, list[int]]           =       {}
				for i in range(lowercase     ):
								__lowerCamelCase		:   Any           =       []

				for e in range(lowercase     ):
								__lowerCamelCase    ,       __lowerCamelCase		:   Dict           =       (int(lowercase     ) for i in _input(F'Edge {e + 1}: <node1> <node2> '     ))
								graph[x].append(lowercase     )
								graph[y].append(lowercase     )
				return graph





def 				a_							(    lowercase				,    lowercase     )      ->dict[int, list[tuple[int, int]]]:






				'''simple docstring'''

				__lowerCamelCase		:   dict[int, list[tuple[int, int]]]           =       {}
				for i in range(lowercase     ):
								__lowerCamelCase		:   List[Any]           =       []

				for e in range(lowercase     ):
								__lowerCamelCase    ,       __lowerCamelCase    ,       __lowerCamelCase		:   int           =       (int(lowercase     ) for i in _input(F'Edge {e + 1}: <node1> <node2> <weight> '     ))
								graph[x].append((y, w)     )
								graph[y].append((x, w)     )
				return graph


if __name__ == "__main__":
				__lowercase		,		__lowercase	:   List[Any]   		=					(int(i) for i in _input("""Number of nodes and edges: """))

				__lowercase	:   Any   		=					int(
				    _input(
				        """Press 1 or 2 or 3 \n"""
				        """1. Unweighted directed \n"""
				        """2. Unweighted undirected \n"""
				        """3. Weighted undirected \n"""
				    )[0]
				)

				__lowercase	:   Any   		=					{
				    1: initialize_unweighted_directed_graph,
				    2: initialize_unweighted_undirected_graph,
				    3: initialize_weighted_undirected_graph,
				}[graph_choice](n, m)





def 				a_							(    lowercase				,    lowercase     )      ->Tuple:






				'''simple docstring'''

				__lowerCamelCase    ,       __lowerCamelCase		:   Dict           =       {s}, [s]
				print(lowercase     )
				while _s:
								__lowerCamelCase		:   int           =       0
								for i in g[_s[-1]]:
												if i not in vis:
																_s.append(lowercase     )
																vis.add(lowercase     )
																__lowerCamelCase		:   Tuple           =       1
																print(lowercase     )
																break
								if not flag:
												_s.pop()





def 				a_							(    lowercase				,    lowercase     )      ->List[str]:






				'''simple docstring'''

				__lowerCamelCase    ,       __lowerCamelCase		:   Tuple           =       {s}, deque([s]     )
				print(lowercase     )
				while q:
								__lowerCamelCase		:   Optional[Any]           =       q.popleft()
								for v in g[u]:
												if v not in vis:
																vis.add(lowercase     )
																q.append(lowercase     )
																print(lowercase     )





def 				a_							(    lowercase				,    lowercase     )      ->Any:






				'''simple docstring'''

				__lowerCamelCase    ,       __lowerCamelCase    ,       __lowerCamelCase		:   Optional[int]           =       {s: 0}, set(), {s: 0}
				while True:
								if len(lowercase     ) == len(lowercase     ) - 1:
												break
								__lowerCamelCase		:   str           =       10_0000
								for i in dist:
												if i not in known and dist[i] < mini:
																__lowerCamelCase		:   Any           =       dist[i]
																__lowerCamelCase		:   List[str]           =       i
								known.add(lowercase     )
								for v in g[u]:
												if v[0] not in known and dist[u] + v[1] < dist.get(v[0]				,    10_0000     ):
																__lowerCamelCase		:   Optional[int]           =       dist[u] + v[1]
																__lowerCamelCase		:   List[str]           =       u
				for i in dist:
								if i != s:
												print(dist[i]     )





def 				a_							(    lowercase				,    lowercase=None				,    lowercase=None     )      ->Optional[Any]:






				'''simple docstring'''

				if q is None:
								__lowerCamelCase		:   int           =       [1]
				if ind is None:
								__lowerCamelCase		:   Any           =       [0] * (len(lowercase     ) + 1)  # SInce oth Index is ignored
								for u in g:
												for v in g[u]:
																ind[v] += 1
								__lowerCamelCase		:   Tuple           =       deque()
								for i in g:
												if ind[i] == 0:
																q.append(lowercase     )
				if len(lowercase     ) == 0:
								return
				__lowerCamelCase		:   Optional[Any]           =       q.popleft()
				print(lowercase     )
				for w in g[v]:
								ind[w] -= 1
								if ind[w] == 0:
												q.append(lowercase     )
				topo(lowercase				,    lowercase				,    lowercase     )





def 				a_							(    )      ->Union[str, Any]:






				'''simple docstring'''

				__lowerCamelCase		:   Tuple           =       input().strip()
				__lowerCamelCase		:   Any           =       []
				for _ in range(lowercase     ):
								a.append(map(lowercase				,    input().strip().split()     )     )
				return a, n





def 				a_							(    lowercase     )      ->List[str]:






				'''simple docstring'''

				((__lowerCamelCase)    ,       (__lowerCamelCase))		:   Optional[int]           =       a_and_n
				__lowerCamelCase		:   Optional[int]           =       list(lowercase     )
				__lowerCamelCase		:   str           =       [[0] * n for i in range(lowercase     )]
				for k in range(lowercase     ):
								for i in range(lowercase     ):
												for j in range(lowercase     ):
																if dist[i][j] > dist[i][k] + dist[k][j]:
																				__lowerCamelCase		:   str           =       dist[i][k] + dist[k][j]
																				__lowerCamelCase		:   Tuple           =       k
				print(lowercase     )





def 				a_							(    lowercase				,    lowercase     )      ->Dict:






				'''simple docstring'''

				__lowerCamelCase    ,       __lowerCamelCase    ,       __lowerCamelCase		:   int           =       {s: 0}, set(), {s: 0}
				while True:
								if len(lowercase     ) == len(lowercase     ) - 1:
												break
								__lowerCamelCase		:   List[Any]           =       10_0000
								for i in dist:
												if i not in known and dist[i] < mini:
																__lowerCamelCase		:   str           =       dist[i]
																__lowerCamelCase		:   Optional[int]           =       i
								known.add(lowercase     )
								for v in g[u]:
												if v[0] not in known and v[1] < dist.get(v[0]				,    10_0000     ):
																__lowerCamelCase		:   Dict           =       v[1]
																__lowerCamelCase		:   List[str]           =       u
				return dist





def 				a_							(    )      ->Union[str, Any]:






				'''simple docstring'''

				__lowerCamelCase    ,       __lowerCamelCase		:   List[Any]           =       map(lowercase				,    input().split(" "     )     )
				__lowerCamelCase		:   Optional[Any]           =       []
				for _ in range(lowercase     ):
								edges.append(map(lowercase				,    input().split(" "     )     )     )
				return edges, n





def 				a_							(    lowercase     )      ->Optional[int]:






				'''simple docstring'''

				((__lowerCamelCase)    ,       (__lowerCamelCase))		:   Any           =       e_and_n
				e.sort(reverse=lowercase				,    key=lambda lowercase     : x[2]     )
				__lowerCamelCase		:   Optional[Any]           =       [{i} for i in range(1				,    n + 1     )]
				while True:
								if len(lowercase     ) == 1:
												break
								print(lowercase     )
								__lowerCamelCase		:   List[str]           =       e.pop()
								for i in range(len(lowercase     )     ):
												if x[0] in s[i]:
																break
								for j in range(len(lowercase     )     ):
												if x[1] in s[j]:
																if i == j:
																				break
																s[j].update(s[i]     )
																s.pop(lowercase     )
																break





def 				a_							(    lowercase     )      ->int:






				'''simple docstring'''

				__lowerCamelCase		:   Tuple           =       []
				for node in graph:
								if not graph[node]:
												isolated.append(lowercase     )
				return isolated





