

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







class 						__magic_name__			(							lowerCAmelCase_							):

   '''simple docstring'''




   def __init__(				self,    lowercase_,    lowercase_,    lowercase_,    lowercase_,    lowercase_,    lowercase_,    lowercase_,    )							->    Optional[int]:






     """simple docstring"""






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



   def  _UpperCAmelCase (				self,    lowercase_ = "auto"       )							->    Union[str, Any]:






     """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(__a       )



   def  _UpperCAmelCase (				self       )							->    Any:






     """simple docstring"""






     self.enable_attention_slicing(__a       )



   @torch.no_grad()
   def __call__(				self,    lowercase_,    lowercase_ = 512,    lowercase_ = 512,    lowercase_ = 50,    lowercase_ = 7.5,    lowercase_ = None,    lowercase_ = 1,    lowercase_ = 0.0,    lowercase_ = None,    lowercase_ = None,    lowercase_ = "pil",    lowercase_ = True,    lowercase_ = None,    lowercase_ = 1,    lowercase_ = None,    **lowercase_,    )							->    Dict:






     """simple docstring"""






     if isinstance(__a,    __a       ):
       a__  =1
     elif isinstance(__a,    __a       ):
       a__  =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
     a__  =self.tokenizer(
         __a,    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__  =text_embeddings.shape
     a__  =text_embeddings.repeat(1,    __a,    1       )
     a__  =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.
     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(__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       ):
         a__  =[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:
         a__  =negative_prompt

       a__  =text_input_ids.shape[-1]
       a__  =self.tokenizer(
           __a,    padding='''max_length''',    max_length=__a,    truncation=__a,    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(__a,    __a,    1       )
       a__  =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
       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(
             __a,    generator=__a,    device='''cpu''',    dtype=__a       ).to(self.device       )
         a__  =torch.randn(__a,    generator=__a,    device='''cpu''',    dtype=__a       ).to(
             self.device       )
       else:
         a__  =torch.randn(
             __a,    generator=__a,    device=self.device,    dtype=__a       )
         a__  =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}"""       )
       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(__a       )

     # 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(__a       )       ):
       # 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(__a,    __a       )

       # predict the noise residual
       a__  =self.unet(__a,    __a,    encoder_hidden_states=__a       ).sample

       # perform guidance
       if do_classifier_free_guidance:
         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(__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       )

     a__  =1 / 0.18215 * latents
     a__  =self.vae.decode(__a       ).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(__a       ),    return_tensors='''pt'''       ).to(
           self.device       )
       a__  =self.safety_checker(
           images=__a,    clip_input=safety_checker_input.pixel_values.to(text_embeddings.dtype       )       )
     else:
       a__  =None

     if output_type == "pil":
       a__  =self.numpy_to_pil(__a       )

     if not return_dict:
       return (image, has_nsfw_concept)

     return StableDiffusionPipelineOutput(images=__a,    nsfw_content_detected=__a       )




'''simple docstring'''



from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE      :   int   ):
					__a			:       int					    =  int(number**0.5   )
					return number == sq * sq






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int   ):
					__a			:       int					    =  x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
					__a			:       int					    =  x_den * y_den * z_den
					__a			:       int					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
					top //= hcf
					bottom //= hcf
					return top, bottom






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE      :   int = 35   ):
					__a			:       set					    =  set()
					__a			:       int
					__a			:       Fraction					    =  Fraction(0   )
					__a			:       tuple[int, int]

					for x_num in range(1						,      order + 1   ):
										for x_den in range(x_num + 1						,      order + 1   ):
															for y_num in range(1						,      order + 1   ):
																				for y_den in range(y_num + 1						,      order + 1   ):
																									# n=1
																									__a			:       Union[str, Any]					    =  x_num * y_den + x_den * y_num
																									__a			:       Optional[Any]					    =  x_den * y_den
																									__a			:       int					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																									z_num //= hcf
																									z_den //= hcf
																									if 0 < z_num < z_den <= order:
																														__a			:       Any					    =  add_three(
																														    _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																														unique_s.add(_SCREAMING_SNAKE_CASE   )

																									# n=2
																									__a			:       Optional[int]					    =  (
																									    x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
																									)
																									__a			:       Union[str, Any]					    =  x_den * x_den * y_den * y_den
																									if is_sq(_SCREAMING_SNAKE_CASE   ) and is_sq(_SCREAMING_SNAKE_CASE   ):
																														__a			:       List[Any]					    =  int(sqrt(_SCREAMING_SNAKE_CASE   )   )
																														__a			:       Any					    =  int(sqrt(_SCREAMING_SNAKE_CASE   )   )
																														__a			:       Optional[int]					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																														z_num //= hcf
																														z_den //= hcf
																														if 0 < z_num < z_den <= order:
																																			__a			:       List[Any]					    =  add_three(
																																			    _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																																			unique_s.add(_SCREAMING_SNAKE_CASE   )

                    # n=-1
																									__a			:       int					    =  x_num * y_num
																									__a			:       Optional[Any]					    =  x_den * y_num + x_num * y_den
																									__a			:       Tuple					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																									z_num //= hcf
																									z_den //= hcf
																									if 0 < z_num < z_den <= order:
																														__a			:       Any					    =  add_three(
																														    _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																														unique_s.add(_SCREAMING_SNAKE_CASE   )

																									# n=2
																									__a			:       List[Any]					    =  x_num * x_num * y_num * y_num
																									__a			:       List[Any]					    =  (
																									    x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
																									)
																									if is_sq(_SCREAMING_SNAKE_CASE   ) and is_sq(_SCREAMING_SNAKE_CASE   ):
																														__a			:       Optional[Any]					    =  int(sqrt(_SCREAMING_SNAKE_CASE   )   )
																														__a			:       Union[str, Any]					    =  int(sqrt(_SCREAMING_SNAKE_CASE   )   )
																														__a			:       int					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																														z_num //= hcf
																														z_den //= hcf
																														if 0 < z_num < z_den <= order:
																																			__a			:       List[str]					    =  add_three(
																																			    _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																																			unique_s.add(_SCREAMING_SNAKE_CASE   )

					for num, den in unique_s:
										total += Fraction(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )

					return total.denominator + total.numerator


if __name__ == "__main__":
	print(f'''{solution() = }''')



