




import inspect
from typing import List, Optional, Union

import torch
from torch import nn
from torch.nn import functional as F
from torchvision import transforms
from transformers import CLIPImageProcessor, CLIPModel, CLIPTextModel, CLIPTokenizer

from diffusers import (
    AutoencoderKL,
    DDIMScheduler,
    DiffusionPipeline,
    DPMSolverMultistepScheduler,
    LMSDiscreteScheduler,
    PNDMScheduler,
    UNetaDConditionModel,
)
from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion import StableDiffusionPipelineOutput
class       __a					( nn.Module     ):


     """simple docstring"""


     def __init__(	self			: Optional[Any]				,_UpperCamelCase			: Any				,_UpperCamelCase			: Tuple=1.0						)		->   int:


         '''simple docstring'''





         super().__init__()

         SCREAMING_SNAKE_CASE__								=cut_size
         SCREAMING_SNAKE_CASE__								=cut_power




     def   __A				(	self			: Optional[Any]				,_UpperCamelCase			: str				,_UpperCamelCase			: Optional[Any]						)		->   Tuple:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__			,		SCREAMING_SNAKE_CASE__								=pixel_values.shape[2:4]
         SCREAMING_SNAKE_CASE__								=min(_UpperCamelCase				,_UpperCamelCase						)
         SCREAMING_SNAKE_CASE__								=min(_UpperCamelCase				,_UpperCamelCase				,self.cut_size						)
         SCREAMING_SNAKE_CASE__								=[]
         for _ in range(_UpperCamelCase						):
             SCREAMING_SNAKE_CASE__								=int(torch.rand([]						) ** self.cut_power * (max_size - min_size) + min_size						)
             SCREAMING_SNAKE_CASE__								=torch.randint(0				,sideX - size + 1				,()						)
             SCREAMING_SNAKE_CASE__								=torch.randint(0				,sideY - size + 1				,()						)
             SCREAMING_SNAKE_CASE__								=pixel_values[:, :, offsety : offsety + size, offsetx : offsetx + size]
             cutouts.append(F.adaptive_avg_poolad(_UpperCamelCase				,self.cut_size						)						)
         return torch.cat(_UpperCamelCase						)






def 	UpperCAmelCase_    (	__UpperCamelCase,				__UpperCamelCase	):
    SCREAMING_SNAKE_CASE__								=F.normalize(__UpperCamelCase,				dim=-1	)
    SCREAMING_SNAKE_CASE__								=F.normalize(__UpperCamelCase,				dim=-1	)
    return (x - y).norm(dim=-1	).div(2	).arcsin().pow(2	).mul(2	)



def 	UpperCAmelCase_    (	__UpperCamelCase,				__UpperCamelCase	):
    for param in model.parameters():
        SCREAMING_SNAKE_CASE__								=value




class       __a					( __lowerCamelCase     ):


     """simple docstring"""


     def __init__(	self			: Optional[Any]				,_UpperCamelCase			: AutoencoderKL				,_UpperCamelCase			: CLIPTextModel				,_UpperCamelCase			: CLIPModel				,_UpperCamelCase			: CLIPTokenizer				,_UpperCamelCase			: UNetaDConditionModel				,_UpperCamelCase			: Union[PNDMScheduler, LMSDiscreteScheduler, DDIMScheduler, DPMSolverMultistepScheduler]				,_UpperCamelCase			: CLIPImageProcessor				,)		->   List[Any]:


         '''simple docstring'''





         super().__init__()
         self.register_modules(
             vae=_UpperCamelCase				,text_encoder=_UpperCamelCase				,clip_model=_UpperCamelCase				,tokenizer=_UpperCamelCase				,unet=_UpperCamelCase				,scheduler=_UpperCamelCase				,feature_extractor=_UpperCamelCase				,)

         SCREAMING_SNAKE_CASE__								=transforms.Normalize(mean=feature_extractor.image_mean				,std=feature_extractor.image_std						)
         SCREAMING_SNAKE_CASE__								=(
             feature_extractor.size
             if isinstance(feature_extractor.size				,_UpperCamelCase						)
             else feature_extractor.size["""shortest_edge"""]
         )
         SCREAMING_SNAKE_CASE__								=MakeCutouts(self.cut_out_size						)

         set_requires_grad(self.text_encoder				,_UpperCamelCase						)
         set_requires_grad(self.clip_model				,_UpperCamelCase						)




     def   __A				(	self			: Optional[int]				,_UpperCamelCase			: Optional[Union[str, int]] = "auto"						)		->   Tuple:


         '''simple docstring'''





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




     def   __A				(	self			: str						)		->   str:


         '''simple docstring'''





         self.enable_attention_slicing(_UpperCamelCase						)




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


         '''simple docstring'''





         set_requires_grad(self.vae				,_UpperCamelCase						)




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


         '''simple docstring'''





         set_requires_grad(self.vae				,_UpperCamelCase						)




     def   __A				(	self			: Optional[Any]						)		->   List[Any]:


         '''simple docstring'''





         set_requires_grad(self.unet				,_UpperCamelCase						)




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


         '''simple docstring'''





         set_requires_grad(self.unet				,_UpperCamelCase						)




     @torch.enable_grad()
     def   __A				(	self			: Optional[Any]				,_UpperCamelCase			: int				,_UpperCamelCase			: Optional[Any]				,_UpperCamelCase			: List[str]				,_UpperCamelCase			: List[Any]				,_UpperCamelCase			: int				,_UpperCamelCase			: str				,_UpperCamelCase			: Tuple				,_UpperCamelCase			: int				,_UpperCamelCase			: Tuple=True				,)		->   Tuple:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=latents.detach().requires_grad_()

         SCREAMING_SNAKE_CASE__								=self.scheduler.scale_model_input(_UpperCamelCase				,_UpperCamelCase						)

         # predict the noise residual
         SCREAMING_SNAKE_CASE__								=self.unet(_UpperCamelCase				,_UpperCamelCase				,encoder_hidden_states=_UpperCamelCase						).sample

         if isinstance(self.scheduler				,(PNDMScheduler, DDIMScheduler, DPMSolverMultistepScheduler)						):
             SCREAMING_SNAKE_CASE__								=self.scheduler.alphas_cumprod[timestep]
             SCREAMING_SNAKE_CASE__								=1 - alpha_prod_t
             # compute predicted original sample from predicted noise also called
             # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
             SCREAMING_SNAKE_CASE__								=(latents - beta_prod_t ** 0.5 * noise_pred) / alpha_prod_t ** 0.5

             SCREAMING_SNAKE_CASE__								=torch.sqrt(_UpperCamelCase						)
             SCREAMING_SNAKE_CASE__								=pred_original_sample * (fac) + latents * (1 - fac)
         elif isinstance(self.scheduler				,_UpperCamelCase						):
             SCREAMING_SNAKE_CASE__								=self.scheduler.sigmas[index]
             SCREAMING_SNAKE_CASE__								=latents - sigma * noise_pred
         else:
             raise ValueError(f"""scheduler type {type(self.scheduler						)} not supported"""						)

         SCREAMING_SNAKE_CASE__								=1 / self.vae.config.scaling_factor * sample
         SCREAMING_SNAKE_CASE__								=self.vae.decode(_UpperCamelCase						).sample
         SCREAMING_SNAKE_CASE__								=(image / 2 + 0.5).clamp(0				,1						)

         if use_cutouts:
             SCREAMING_SNAKE_CASE__								=self.make_cutouts(_UpperCamelCase				,_UpperCamelCase						)
         else:
             SCREAMING_SNAKE_CASE__								=transforms.Resize(self.cut_out_size						)(_UpperCamelCase						)
         SCREAMING_SNAKE_CASE__								=self.normalize(_UpperCamelCase						).to(latents.dtype						)

         SCREAMING_SNAKE_CASE__								=self.clip_model.get_image_features(_UpperCamelCase						)
         SCREAMING_SNAKE_CASE__								=image_embeddings_clip / image_embeddings_clip.norm(p=2				,dim=-1				,keepdim=_UpperCamelCase						)

         if use_cutouts:
             SCREAMING_SNAKE_CASE__								=spherical_dist_loss(_UpperCamelCase				,_UpperCamelCase						)
             SCREAMING_SNAKE_CASE__								=dists.view([num_cutouts, sample.shape[0], -1]						)
             SCREAMING_SNAKE_CASE__								=dists.sum(2						).mean(0						).sum() * clip_guidance_scale
         else:
             SCREAMING_SNAKE_CASE__								=spherical_dist_loss(_UpperCamelCase				,_UpperCamelCase						).mean() * clip_guidance_scale

         SCREAMING_SNAKE_CASE__								=-torch.autograd.grad(_UpperCamelCase				,_UpperCamelCase						)[0]

         if isinstance(self.scheduler				,_UpperCamelCase						):
             SCREAMING_SNAKE_CASE__								=latents.detach() + grads * (sigma**2)
             SCREAMING_SNAKE_CASE__								=noise_pred_original
         else:
             SCREAMING_SNAKE_CASE__								=noise_pred_original - torch.sqrt(_UpperCamelCase						) * grads
         return noise_pred, latents




     @torch.no_grad()
     def __call__(	self			: Optional[int]				,_UpperCamelCase			: Union[str, List[str]]				,_UpperCamelCase			: Optional[int] = 5_1_2				,_UpperCamelCase			: Optional[int] = 5_1_2				,_UpperCamelCase			: Optional[int] = 5_0				,_UpperCamelCase			: Optional[float] = 7.5				,_UpperCamelCase			: Optional[int] = 1				,_UpperCamelCase			: float = 0.0				,_UpperCamelCase			: Optional[float] = 1_0_0				,_UpperCamelCase			: Optional[Union[str, List[str]]] = None				,_UpperCamelCase			: Optional[int] = 4				,_UpperCamelCase			: Optional[bool] = True				,_UpperCamelCase			: Optional[torch.Generator] = None				,_UpperCamelCase			: Optional[torch.FloatTensor] = None				,_UpperCamelCase			: Optional[str] = "pil"				,_UpperCamelCase			: bool = True				,)		->   int:


         '''simple docstring'''





         if isinstance(_UpperCamelCase				,_UpperCamelCase						):
             SCREAMING_SNAKE_CASE__								=1
         elif isinstance(_UpperCamelCase				,_UpperCamelCase						):
             SCREAMING_SNAKE_CASE__								=len(_UpperCamelCase						)
         else:
             raise ValueError(f"""`prompt` has to be of type `str` or `list` but is {type(_UpperCamelCase						)}"""						)

         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}."""						)

         # get prompt text embeddings
         SCREAMING_SNAKE_CASE__								=self.tokenizer(
             _UpperCamelCase				,padding="""max_length"""				,max_length=self.tokenizer.model_max_length				,truncation=_UpperCamelCase				,return_tensors="""pt"""				,)
         SCREAMING_SNAKE_CASE__								=self.text_encoder(text_input.input_ids.to(self.device						)						)[0]
         # duplicate text embeddings for each generation per prompt
         SCREAMING_SNAKE_CASE__								=text_embeddings.repeat_interleave(_UpperCamelCase				,dim=0						)

         if clip_guidance_scale > 0:
             if clip_prompt is not None:
                 SCREAMING_SNAKE_CASE__								=self.tokenizer(
                     _UpperCamelCase				,padding="""max_length"""				,max_length=self.tokenizer.model_max_length				,truncation=_UpperCamelCase				,return_tensors="""pt"""				,).input_ids.to(self.device						)
             else:
                 SCREAMING_SNAKE_CASE__								=text_input.input_ids.to(self.device						)
             SCREAMING_SNAKE_CASE__								=self.clip_model.get_text_features(_UpperCamelCase						)
             SCREAMING_SNAKE_CASE__								=text_embeddings_clip / text_embeddings_clip.norm(p=2				,dim=-1				,keepdim=_UpperCamelCase						)
             # duplicate text embeddings clip for each generation per prompt
             SCREAMING_SNAKE_CASE__								=text_embeddings_clip.repeat_interleave(_UpperCamelCase				,dim=0						)

         # 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.
         SCREAMING_SNAKE_CASE__								=guidance_scale > 1.0
         # get unconditional embeddings for classifier free guidance
         if do_classifier_free_guidance:
             SCREAMING_SNAKE_CASE__								=text_input.input_ids.shape[-1]
             SCREAMING_SNAKE_CASE__								=self.tokenizer([""""""]				,padding="""max_length"""				,max_length=_UpperCamelCase				,return_tensors="""pt"""						)
             SCREAMING_SNAKE_CASE__								=self.text_encoder(uncond_input.input_ids.to(self.device						)						)[0]
             # duplicate unconditional embeddings for each generation per prompt
             SCREAMING_SNAKE_CASE__								=uncond_embeddings.repeat_interleave(_UpperCamelCase				,dim=0						)

             # 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
             SCREAMING_SNAKE_CASE__								=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`.
         SCREAMING_SNAKE_CASE__								=(batch_size * num_images_per_prompt, self.unet.config.in_channels, height // 8, width // 8)
         SCREAMING_SNAKE_CASE__								=text_embeddings.dtype
         if latents is None:
             if self.device.type == "mps":
                 # randn does not work reproducibly on mps
                 SCREAMING_SNAKE_CASE__								=torch.randn(_UpperCamelCase				,generator=_UpperCamelCase				,device="""cpu"""				,dtype=_UpperCamelCase						).to(
                     self.device						)
             else:
                 SCREAMING_SNAKE_CASE__								=torch.randn(_UpperCamelCase				,generator=_UpperCamelCase				,device=self.device				,dtype=_UpperCamelCase						)
         else:
             if latents.shape != latents_shape:
                 raise ValueError(f"""Unexpected latents shape, got {latents.shape}, expected {latents_shape}"""						)
             SCREAMING_SNAKE_CASE__								=latents.to(self.device						)

         # set timesteps
         SCREAMING_SNAKE_CASE__								="""offset""" in set(inspect.signature(self.scheduler.set_timesteps						).parameters.keys()						)
         SCREAMING_SNAKE_CASE__								={}
         if accepts_offset:
             SCREAMING_SNAKE_CASE__								=1

         self.scheduler.set_timesteps(_UpperCamelCase				,**_UpperCamelCase						)

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

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

         # check if the scheduler accepts generator
         SCREAMING_SNAKE_CASE__								="""generator""" in set(inspect.signature(self.scheduler.step						).parameters.keys()						)
         if accepts_generator:
             SCREAMING_SNAKE_CASE__								=generator

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

             # predict the noise residual
             SCREAMING_SNAKE_CASE__								=self.unet(_UpperCamelCase				,_UpperCamelCase				,encoder_hidden_states=_UpperCamelCase						).sample

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

             # perform clip guidance
             if clip_guidance_scale > 0:
                 SCREAMING_SNAKE_CASE__								=(
                     text_embeddings.chunk(2						)[1] if do_classifier_free_guidance else text_embeddings
                 )
                 SCREAMING_SNAKE_CASE__			,		SCREAMING_SNAKE_CASE__								=self.cond_fn(
                     _UpperCamelCase				,_UpperCamelCase				,_UpperCamelCase				,_UpperCamelCase				,_UpperCamelCase				,_UpperCamelCase				,_UpperCamelCase				,_UpperCamelCase				,_UpperCamelCase				,)

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

         # scale and decode the image latents with vae
         SCREAMING_SNAKE_CASE__								=1 / self.vae.config.scaling_factor * latents
         SCREAMING_SNAKE_CASE__								=self.vae.decode(_UpperCamelCase						).sample

         SCREAMING_SNAKE_CASE__								=(image / 2 + 0.5).clamp(0				,1						)
         SCREAMING_SNAKE_CASE__								=image.cpu().permute(0				,2				,3				,1						).numpy()

         if output_type == "pil":
             SCREAMING_SNAKE_CASE__								=self.numpy_to_pil(_UpperCamelCase						)

         if not return_dict:
             return (image, None)

         return StableDiffusionPipelineOutput(images=_UpperCamelCase				,nsfw_content_detected=_UpperCamelCase						)












def 	UpperCAmelCase_    (	__UpperCamelCase,				__UpperCamelCase	):
    SCREAMING_SNAKE_CASE__								=1.0
    for i in range(1,				r + 1	):
        ret *= (n + 1 - i) / i
    return round(__UpperCamelCase	)



def 	UpperCAmelCase_    (	__UpperCamelCase	):
    return choose(8 + n,				__UpperCamelCase	) + choose(9 + n,				__UpperCamelCase	) - 10



def 	UpperCAmelCase_    (	__UpperCamelCase	):
    return sum(non_bouncy_exact(__UpperCamelCase	) for i in range(1,				n + 1	)	)



def 	UpperCAmelCase_    (	__UpperCamelCase = 100	):
    return non_bouncy_upto(__UpperCamelCase	)


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






