



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


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


class   __lowerCAmelCase  (		UpperCAmelCase_   ):
					"""simple docstring"""






					def __init__(  self       :							Dict					,       _snake_case       :							AutoencoderKL					,       _snake_case       :							CLIPTextModel					,       _snake_case       :							CLIPTokenizer					,       _snake_case       :							UNetaDConditionModel					,       _snake_case       :							Union[DDIMScheduler, PNDMScheduler, LMSDiscreteScheduler]					,       _snake_case       :							StableDiffusionSafetyChecker					,       _snake_case       :							CLIPImageProcessor					,       ):






								"""simple docstring"""


								super().__init__()
								self.register_modules(
								    vae=_snake_case					,       text_encoder=_snake_case					,       tokenizer=_snake_case					,       unet=_snake_case					,       scheduler=_snake_case					,       safety_checker=_snake_case					,       feature_extractor=_snake_case					,       )



					def      _a				(  self       :							List[Any]					,       _snake_case       :							Optional[Union[str, int]] = "auto"       ):






								"""simple docstring"""


								if slice_size == "auto":
											# half the attention head size is usually a good trade-off between
											# speed and memory
											A__	  =     self.unet.config.attention_head_dim // 2
								self.unet.set_attention_slice(_snake_case       )



					def      _a				(  self       :							str       ):






								"""simple docstring"""


								self.enable_attention_slicing(_snake_case       )



					@torch.no_grad()
					def __call__(  self       :							Optional[int]					,       _snake_case       :							Union[str, List[str]]					,       _snake_case       :							int = 5_12					,       _snake_case       :							int = 5_12					,       _snake_case       :							int = 50					,       _snake_case       :							float = 7.5					,       _snake_case       :							Optional[Union[str, List[str]]] = None					,       _snake_case       :							Optional[int] = 1					,       _snake_case       :							float = 0.0					,       _snake_case       :							Optional[torch.Generator] = None					,       _snake_case       :							Optional[torch.FloatTensor] = None					,       _snake_case       :							Optional[str] = "pil"					,       _snake_case       :							bool = True					,       _snake_case       :							Optional[Callable[[int, int, torch.FloatTensor], None]] = None					,       _snake_case       :							int = 1					,       _snake_case       :							Optional[torch.FloatTensor] = None					,       **_snake_case       :							List[str]					,       ):






								"""simple docstring"""


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

								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(_snake_case					,       _snake_case       ) or callback_steps <= 0)
								):
											raise ValueError(
											    F'''`callback_steps` has to be a positive integer but is {callback_steps} of type'''
											    F''' {type(_snake_case       )}.'''       )

								# get prompt text embeddings
								A__	  =     self.tokenizer(
								    _snake_case					,       padding='max_length'					,       max_length=self.tokenizer.model_max_length					,       return_tensors='pt'					,       )
								A__	  =     text_inputs.input_ids

								if text_input_ids.shape[-1] > self.tokenizer.model_max_length:
											A__	  =     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}'''       )
											A__	  =     text_input_ids[:, : self.tokenizer.model_max_length]

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

								# duplicate text embeddings for each generation per prompt, using mps friendly method
								A__  ,			A__  ,			A__	  =     text_embeddings.shape
								A__	  =     text_embeddings.repeat(1					,       _snake_case					,       1       )
								A__	  =     text_embeddings.view(bs_embed * num_images_per_prompt					,       _snake_case					,       -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.
								A__	  =     guidance_scale > 1.0
								# get unconditional embeddings for classifier free guidance
								if do_classifier_free_guidance:
											A__	  =     42
											if negative_prompt is None:
														A__	  =     ['']
											elif type(_snake_case       ) is not type(_snake_case       ):
														raise TypeError(
														    F'''`negative_prompt` should be the same type to `prompt`, but got {type(_snake_case       )} !='''
														    F''' {type(_snake_case       )}.'''       )
											elif isinstance(_snake_case					,       _snake_case       ):
														A__	  =     [negative_prompt]
											elif batch_size != len(_snake_case       ):
														raise ValueError(
														    F'''`negative_prompt`: {negative_prompt} has batch size {len(_snake_case       )}, but `prompt`:'''
														    F''' {prompt} has batch size {batch_size}. Please make sure that passed `negative_prompt` matches'''
														    ' the batch size of `prompt`.'       )
											else:
														A__	  =     negative_prompt

											A__	  =     text_input_ids.shape[-1]
											A__	  =     self.tokenizer(
											    _snake_case					,       padding='max_length'					,       max_length=_snake_case					,       truncation=_snake_case					,       return_tensors='pt'					,       )
											A__	  =     self.text_encoder(uncond_input.input_ids.to(self.device       )       )[0]

											# duplicate unconditional embeddings for each generation per prompt, using mps friendly method
											A__	  =     uncond_embeddings.shape[1]
											A__	  =     uncond_embeddings.repeat(_snake_case					,       _snake_case					,       1       )
											A__	  =     uncond_embeddings.view(batch_size * num_images_per_prompt					,       _snake_case					,       -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
											A__	  =     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`.
								A__	  =     (batch_size * num_images_per_prompt, self.unet.config.in_channels, height // 8, width // 8)
								A__	  =     (batch_size * num_images_per_prompt, self.unet.config.in_channels, 64, 64)
								A__	  =     text_embeddings.dtype
								if latents is None:
											if self.device.type == "mps":
														# randn does not exist on mps
														A__	  =     torch.randn(
														    _snake_case					,       generator=_snake_case					,       device='cpu'					,       dtype=_snake_case       ).to(self.device       )
														A__	  =     torch.randn(_snake_case					,       generator=_snake_case					,       device='cpu'					,       dtype=_snake_case       ).to(
														    self.device       )
											else:
														A__	  =     torch.randn(
														    _snake_case					,       generator=_snake_case					,       device=self.device					,       dtype=_snake_case       )
														A__	  =     torch.randn(_snake_case					,       generator=_snake_case					,       device=self.device					,       dtype=_snake_case       )
								else:
											if latents_reference.shape != latents_shape:
														raise ValueError(F'''Unexpected latents shape, got {latents.shape}, expected {latents_shape}'''       )
											A__	  =     latents_reference.to(self.device       )
											A__	  =     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
								A__	  =     (latents_shape[3] - latents_shape_reference[3]) // 2
								A__	  =     (latents_shape[2] - latents_shape_reference[2]) // 2
								A__	  =     latents_shape_reference[3] if dx >= 0 else latents_shape_reference[3] + 2 * dx
								A__	  =     latents_shape_reference[2] if dy >= 0 else latents_shape_reference[2] + 2 * dy
								A__	  =     0 if dx < 0 else dx
								A__	  =     0 if dy < 0 else dy
								A__	  =     max(-dx					,       0       )
								A__	  =     max(-dy					,       0       )
								# import pdb
								# pdb.set_trace()
								A__	  =     latents_reference[:, :, dy : dy + h, dx : dx + w]

								# set timesteps
								self.scheduler.set_timesteps(_snake_case       )

								# Some schedulers like PNDM have timesteps as arrays
								# It's more optimized to move all timesteps to correct device beforehand
								A__	  =     self.scheduler.timesteps.to(self.device       )

								# scale the initial noise by the standard deviation required by the scheduler
								A__	  =     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]
								A__	  =     'eta' in set(inspect.signature(self.scheduler.step       ).parameters.keys()       )
								A__	  =     {}
								if accepts_eta:
											A__	  =     eta

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

											# predict the noise residual
											A__	  =     self.unet(_snake_case					,       _snake_case					,       encoder_hidden_states=_snake_case       ).sample

											# perform guidance
											if do_classifier_free_guidance:
														A__  ,			A__	  =     noise_pred.chunk(2       )
														A__	  =     noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)

											# compute the previous noisy sample x_t -> x_t-1
											A__	  =     self.scheduler.step(_snake_case					,       _snake_case					,       _snake_case					,       **_snake_case       ).prev_sample

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

								A__	  =     1 / 0.1_8215 * latents
								A__	  =     self.vae.decode(_snake_case       ).sample

								A__	  =     (image / 2 + 0.5).clamp(0					,       1       )

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

								if self.safety_checker is not None:
											A__	  =     self.feature_extractor(self.numpy_to_pil(_snake_case       )					,       return_tensors='pt'       ).to(
											    self.device       )
											A__  ,			A__	  =     self.safety_checker(
											    images=_snake_case					,       clip_input=safety_checker_input.pixel_values.to(text_embeddings.dtype       )       )
								else:
											A__	  =     None

								if output_type == "pil":
											A__	  =     self.numpy_to_pil(_snake_case       )

								if not return_dict:
											return (image, has_nsfw_concept)

								return StableDiffusionPipelineOutput(images=_snake_case					,       nsfw_content_detected=_snake_case       )









from __future__ import annotations

from fractions import Fraction


def A    (							__UpperCamelCase			,						__UpperCamelCase       )    ->   bool:
			return (
			    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
			)


def A    (							__UpperCamelCase       )    ->   list[str]:
			A__	  =     []
			A__	  =     11
			A__	  =     int('1' + '0' * digit_len       )
			for num in range(__UpperCamelCase			,						__UpperCamelCase       ):
						while den <= 99:
									if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
												if is_digit_cancelling(__UpperCamelCase			,						__UpperCamelCase       ):
															solutions.append(f'''{num}/{den}'''       )
									den += 1
						num += 1
						A__	  =     10
			return solutions


def A    (							__UpperCamelCase = 2       )    ->   int:
			A__	  =     1.0
			for fraction in fraction_list(__UpperCamelCase       ):
						A__	  =     Fraction(__UpperCamelCase       )
						result *= frac.denominator / frac.numerator
			return int(__UpperCamelCase       )


if __name__ == "__main__":
							print(solution())




