




import inspect
from typing import Optional, Union

import numpy as np
import PIL
import torch
from torch.nn import functional as F
from torchvision import transforms
from transformers import CLIPFeatureExtractor, CLIPModel, CLIPTextModel, CLIPTokenizer

from diffusers import (
    AutoencoderKL,
    DDIMScheduler,
    DiffusionPipeline,
    DPMSolverMultistepScheduler,
    LMSDiscreteScheduler,
    PNDMScheduler,
    UNetaDConditionModel,
)
from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion import StableDiffusionPipelineOutput
from diffusers.utils import (
    PIL_INTERPOLATION,
    randn_tensor,
)


def    A						(__A   :    Tuple   ,				__A   :    str   ,				__A   :    Dict       )   ->      int:







     """simple docstring"""


     if isinstance(__A   ,				torch.Tensor       ):
          return image
     elif isinstance(__A   ,				PIL.Image.Image       ):
          UpperCAmelCase_          =							[image]

     if isinstance(image[0]   ,				PIL.Image.Image       ):
          UpperCAmelCase_          =							[np.array(i.resize((w, h)   ,				resample=PIL_INTERPOLATION['''lanczos''']       )       )[None, :] for i in image]
          UpperCAmelCase_          =							np.concatenate(__A   ,				axis=0       )
          UpperCAmelCase_          =							np.array(__A       ).astype(np.floataa       ) / 255.0
          UpperCAmelCase_          =							image.transpose(0   ,				3   ,				1   ,				2       )
          UpperCAmelCase_          =							2.0 * image - 1.0
          UpperCAmelCase_          =							torch.from_numpy(__A       )
     elif isinstance(image[0]   ,				torch.Tensor       ):
          UpperCAmelCase_          =							torch.cat(__A   ,				dim=0       )
     return image


def    A						(__A   :    Dict   ,				__A   :    List[str]   ,				__A   :    Dict   ,				__A   :    Any=0.9_995       )   ->      Optional[Any]:







     """simple docstring"""


     if not isinstance(__A   ,				np.ndarray       ):
          UpperCAmelCase_          =							True
          UpperCAmelCase_          =							va.device
          UpperCAmelCase_          =							va.cpu().numpy()
          UpperCAmelCase_          =							va.cpu().numpy()

     UpperCAmelCase_          =							np.sum(va * va / (np.linalg.norm(__A       ) * np.linalg.norm(__A       ))       )
     if np.abs(__A       ) > DOT_THRESHOLD:
          UpperCAmelCase_          =							(1 - t) * va + t * va
     else:
          UpperCAmelCase_          =							np.arccos(__A       )
          UpperCAmelCase_          =							np.sin(__A       )
          UpperCAmelCase_          =							theta_a * t
          UpperCAmelCase_          =							np.sin(__A       )
          UpperCAmelCase_          =							np.sin(theta_a - theta_t       ) / sin_theta_a
          UpperCAmelCase_          =							sin_theta_t / sin_theta_a
          UpperCAmelCase_          =							sa * va + sa * va

     if inputs_are_torch:
          UpperCAmelCase_          =							torch.from_numpy(__A       ).to(__A       )

     return va


def    A						(__A   :    Dict   ,				__A   :    Optional[int]       )   ->      List[str]:







     """simple docstring"""


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


def    A						(__A   :    Optional[int]   ,				__A   :    int       )   ->      Optional[Any]:







     """simple docstring"""


     for param in model.parameters():
          UpperCAmelCase_          =							value







class __snake_case			(			a		):







   def __init__(      self		:						Union[str, Any]					,						_snake_case		:						AutoencoderKL					,						_snake_case		:						CLIPTextModel					,						_snake_case		:						CLIPModel					,						_snake_case		:						CLIPTokenizer					,						_snake_case		:						UNetaDConditionModel					,						_snake_case		:						Union[PNDMScheduler, LMSDiscreteScheduler, DDIMScheduler, DPMSolverMultistepScheduler]					,						_snake_case		:						CLIPFeatureExtractor					,						_snake_case		:						Any=None					,						_snake_case		:						str=None					,						_snake_case		:						Optional[int]=None					,						):

        """simple docstring"""


        super().__init__()
        self.register_modules(
            vae=_snake_case					,						text_encoder=_snake_case					,						clip_model=_snake_case					,						tokenizer=_snake_case					,						unet=_snake_case					,						scheduler=_snake_case					,						feature_extractor=_snake_case					,						coca_model=_snake_case					,						coca_tokenizer=_snake_case					,						coca_transform=_snake_case					,						)
        UpperCAmelCase_          =							(
            feature_extractor.size
            if isinstance(feature_extractor.size					,						_snake_case)
            else feature_extractor.size['''shortest_edge''']
        )
        UpperCAmelCase_          =							transforms.Normalize(mean=feature_extractor.image_mean					,						std=feature_extractor.image_std)
        set_requires_grad(self.text_encoder					,						_snake_case)
        set_requires_grad(self.clip_model					,						_snake_case)







   def lowerCamelCase						(      self		:						Union[str, 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
             UpperCAmelCase_          =							self.unet.config.attention_head_dim // 2
        self.unet.set_attention_slice(_snake_case)







   def lowerCamelCase						(      self		:						int):

        """simple docstring"""


        self.enable_attention_slicing(_snake_case)







   def lowerCamelCase						(      self		:						int):

        """simple docstring"""


        set_requires_grad(self.vae					,						_snake_case)







   def lowerCamelCase						(      self		:						Any):

        """simple docstring"""


        set_requires_grad(self.vae					,						_snake_case)







   def lowerCamelCase						(      self		:						Optional[int]):

        """simple docstring"""


        set_requires_grad(self.unet					,						_snake_case)







   def lowerCamelCase						(      self		:						int):

        """simple docstring"""


        set_requires_grad(self.unet					,						_snake_case)







   def lowerCamelCase						(      self		:						Dict					,						_snake_case		:						List[str]					,						_snake_case		:						List[str]					,						_snake_case		:						List[Any]):

        """simple docstring"""


        UpperCAmelCase_          =							min(int(num_inference_steps * strength)					,						_snake_case)

        UpperCAmelCase_          =							max(num_inference_steps - init_timestep					,						0)
        UpperCAmelCase_          =							self.scheduler.timesteps[t_start:]

        return timesteps, num_inference_steps - t_start







   def lowerCamelCase						(      self		:						int					,						_snake_case		:						str					,						_snake_case		:						Union[str, Any]					,						_snake_case		:						str					,						_snake_case		:						str					,						_snake_case		:						Tuple					,						_snake_case		:						Tuple=None):

        """simple docstring"""


        if not isinstance(_snake_case					,						torch.Tensor):
             raise ValueError(F"""`image` has to be of type `torch.Tensor` but is {type(_snake_case)}""")

        UpperCAmelCase_          =							image.to(device=_snake_case					,						dtype=_snake_case)

        if isinstance(_snake_case					,						_snake_case):
             UpperCAmelCase_          =							[
                 self.vae.encode(image[i : i + 1]).latent_dist.sample(generator[i]) for i in range(_snake_case)
             ]
             UpperCAmelCase_          =							torch.cat(_snake_case					,						dim=0)
        else:
             UpperCAmelCase_          =							self.vae.encode(_snake_case).latent_dist.sample(_snake_case)

        # Hardcode 0.18215 because stable-diffusion-2-base has not self.vae.config.scaling_factor
        UpperCAmelCase_          =							0.1_8_2_1_5 * init_latents
        UpperCAmelCase_          =							init_latents.repeat_interleave(_snake_case					,						dim=0)

        UpperCAmelCase_          =							randn_tensor(init_latents.shape					,						generator=_snake_case					,						device=_snake_case					,						dtype=_snake_case)

        # get latents
        UpperCAmelCase_          =							self.scheduler.add_noise(_snake_case					,						_snake_case					,						_snake_case)
        UpperCAmelCase_          =							init_latents

        return latents







   def lowerCamelCase						(      self		:						Any					,						_snake_case		:						Optional[Any]):

        """simple docstring"""


        UpperCAmelCase_          =							self.coca_transform(_snake_case).unsqueeze(0)
        with torch.no_grad(), torch.cuda.amp.autocast():
             UpperCAmelCase_          =							self.coca_model.generate(transformed_image.to(device=self.device					,						dtype=self.coca_model.dtype))
        UpperCAmelCase_          =							self.coca_tokenizer.decode(generated[0].cpu().numpy())
        return generated.split('''<end_of_text>''')[0].replace('''<start_of_text>'''					,						'''''').rstrip(''' .,''')







   def lowerCamelCase						(      self		:						Optional[int]					,						_snake_case		:						List[str]					,						_snake_case		:						int):

        """simple docstring"""


        UpperCAmelCase_          =							self.feature_extractor.preprocess(_snake_case)
        UpperCAmelCase_          =							torch.from_numpy(clip_image_input['''pixel_values'''][0]).unsqueeze(0).to(self.device).half()
        UpperCAmelCase_          =							self.clip_model.get_image_features(_snake_case)
        UpperCAmelCase_          =							image_embeddings_clip / image_embeddings_clip.norm(p=2					,						dim=-1					,						keepdim=_snake_case)
        UpperCAmelCase_          =							image_embeddings_clip.repeat_interleave(_snake_case					,						dim=0)
        return image_embeddings_clip







   @torch.enable_grad()
   def lowerCamelCase						(      self		:						Optional[Any]					,						_snake_case		:						Dict					,						_snake_case		:						List[str]					,						_snake_case		:						Optional[int]					,						_snake_case		:						Any					,						_snake_case		:						Any					,						_snake_case		:						List[Any]					,						_snake_case		:						List[str]					,						):

        """simple docstring"""


        UpperCAmelCase_          =							latents.detach().requires_grad_()

        UpperCAmelCase_          =							self.scheduler.scale_model_input(_snake_case					,						_snake_case)

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

        if isinstance(self.scheduler					,						(PNDMScheduler, DDIMScheduler, DPMSolverMultistepScheduler)):
             UpperCAmelCase_          =							self.scheduler.alphas_cumprod[timestep]
             UpperCAmelCase_          =							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
             UpperCAmelCase_          =							(latents - beta_prod_t ** 0.5 * noise_pred) / alpha_prod_t ** 0.5

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

        # Hardcode 0.18215 because stable-diffusion-2-base has not self.vae.config.scaling_factor
        UpperCAmelCase_          =							1 / 0.1_8_2_1_5 * sample
        UpperCAmelCase_          =							self.vae.decode(_snake_case).sample
        UpperCAmelCase_          =							(image / 2 + 0.5).clamp(0					,						1)

        UpperCAmelCase_          =							transforms.Resize(self.feature_extractor_size)(_snake_case)
        UpperCAmelCase_          =							self.normalize(_snake_case).to(latents.dtype)

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

        UpperCAmelCase_          =							spherical_dist_loss(_snake_case					,						_snake_case).mean() * clip_guidance_scale

        UpperCAmelCase_          =							-torch.autograd.grad(_snake_case					,						_snake_case)[0]

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







   @torch.no_grad()
   def __call__(      self		:						List[Any]					,						_snake_case		:						Union[torch.FloatTensor, PIL.Image.Image]					,						_snake_case		:						Union[torch.FloatTensor, PIL.Image.Image]					,						_snake_case		:						Optional[str] = None					,						_snake_case		:						Optional[str] = None					,						_snake_case		:						Optional[int] = 512					,						_snake_case		:						Optional[int] = 512					,						_snake_case		:						float = 0.6					,						_snake_case		:						Optional[int] = 50					,						_snake_case		:						Optional[float] = 7.5					,						_snake_case		:						Optional[int] = 1					,						_snake_case		:						float = 0.0					,						_snake_case		:						Optional[float] = 100					,						_snake_case		:						Optional[torch.Generator] = None					,						_snake_case		:						Optional[str] = "pil"					,						_snake_case		:						bool = True					,						_snake_case		:						float = 0.8					,						_snake_case		:						float = 0.1					,						_snake_case		:						float = 0.1					,						):

        """simple docstring"""


        if isinstance(_snake_case					,						_snake_case) and len(_snake_case) != batch_size:
             raise ValueError(F"""You have passed {batch_size} batch_size, but only {len(_snake_case)} generators.""")

        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 isinstance(_snake_case					,						torch.Generator) and batch_size > 1:
             UpperCAmelCase_          =							[generator] + [None] * (batch_size - 1)

        UpperCAmelCase_          =							[
            ('''model''', self.coca_model is None),
            ('''tokenizer''', self.coca_tokenizer is None),
            ('''transform''', self.coca_transform is None),
        ]
        UpperCAmelCase_          =							[x[0] for x in coca_is_none if x[1]]
        UpperCAmelCase_          =							''', '''.join(_snake_case)
        # generate prompts with coca model if prompt is None
        if content_prompt is None:
             if len(_snake_case):
                  raise ValueError(
                      F"""Content prompt is None and CoCa [{coca_is_none_str}] is None."""
                      F"""Set prompt or pass Coca [{coca_is_none_str}] to DiffusionPipeline.""")
             UpperCAmelCase_          =							self.get_image_description(_snake_case)
        if style_prompt is None:
             if len(_snake_case):
                  raise ValueError(
                      F"""Style prompt is None and CoCa [{coca_is_none_str}] is None."""
                      F""" Set prompt or pass Coca [{coca_is_none_str}] to DiffusionPipeline.""")
             UpperCAmelCase_          =							self.get_image_description(_snake_case)

        # get prompt text embeddings for content and style
        UpperCAmelCase_          =							self.tokenizer(
            _snake_case					,						padding='''max_length'''					,						max_length=self.tokenizer.model_max_length					,						truncation=_snake_case					,						return_tensors='''pt'''					,						)
        UpperCAmelCase_          =							self.text_encoder(content_text_input.input_ids.to(self.device))[0]

        UpperCAmelCase_          =							self.tokenizer(
            _snake_case					,						padding='''max_length'''					,						max_length=self.tokenizer.model_max_length					,						truncation=_snake_case					,						return_tensors='''pt'''					,						)
        UpperCAmelCase_          =							self.text_encoder(style_text_input.input_ids.to(self.device))[0]

        UpperCAmelCase_          =							slerp(_snake_case					,						_snake_case					,						_snake_case)

        # duplicate text embeddings for each generation per prompt
        UpperCAmelCase_          =							text_embeddings.repeat_interleave(_snake_case					,						dim=0)

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

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

        UpperCAmelCase_     ,       UpperCAmelCase_          =							self.get_timesteps(_snake_case					,						_snake_case					,						self.device)
        UpperCAmelCase_          =							timesteps[:1].repeat(_snake_case)

        # Preprocess image
        UpperCAmelCase_          =							preprocess(_snake_case					,						_snake_case					,						_snake_case)
        UpperCAmelCase_          =							self.prepare_latents(
            _snake_case					,						_snake_case					,						_snake_case					,						text_embeddings.dtype					,						self.device					,						_snake_case)

        UpperCAmelCase_          =							preprocess(_snake_case					,						_snake_case					,						_snake_case)
        UpperCAmelCase_          =							self.prepare_latents(
            _snake_case					,						_snake_case					,						_snake_case					,						text_embeddings.dtype					,						self.device					,						_snake_case)

        UpperCAmelCase_          =							slerp(_snake_case					,						_snake_case					,						_snake_case)

        if clip_guidance_scale > 0:
             UpperCAmelCase_          =							self.get_clip_image_embeddings(_snake_case					,						_snake_case)
             UpperCAmelCase_          =							self.get_clip_image_embeddings(_snake_case					,						_snake_case)
             UpperCAmelCase_          =							slerp(
                 _snake_case					,						_snake_case					,						_snake_case)

        # 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.
        UpperCAmelCase_          =							guidance_scale > 1.0
        # get unconditional embeddings for classifier free guidance
        if do_classifier_free_guidance:
             UpperCAmelCase_          =							content_text_input.input_ids.shape[-1]
             UpperCAmelCase_          =							self.tokenizer(['''''']					,						padding='''max_length'''					,						max_length=_snake_case					,						return_tensors='''pt''')
             UpperCAmelCase_          =							self.text_encoder(uncond_input.input_ids.to(self.device))[0]
             # duplicate unconditional embeddings for each generation per prompt
             UpperCAmelCase_          =							uncond_embeddings.repeat_interleave(_snake_case					,						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
             UpperCAmelCase_          =							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`.
        UpperCAmelCase_          =							(batch_size, self.unet.config.in_channels, height // 8, width // 8)
        UpperCAmelCase_          =							text_embeddings.dtype
        if latents is None:
             if self.device.type == "mps":
                  # randn does not work reproducibly on mps
                  UpperCAmelCase_          =							torch.randn(_snake_case					,						generator=_snake_case					,						device='''cpu'''					,						dtype=_snake_case).to(
                      self.device)
             else:
                  UpperCAmelCase_          =							torch.randn(_snake_case					,						generator=_snake_case					,						device=self.device					,						dtype=_snake_case)
        else:
             if latents.shape != latents_shape:
                  raise ValueError(F"""Unexpected latents shape, got {latents.shape}, expected {latents_shape}""")
             UpperCAmelCase_          =							latents.to(self.device)

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

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

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

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

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

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

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

        # Hardcode 0.18215 because stable-diffusion-2-base has not self.vae.config.scaling_factor
        UpperCAmelCase_          =							1 / 0.1_8_2_1_5 * latents
        UpperCAmelCase_          =							self.vae.decode(_snake_case).sample

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

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

        if not return_dict:
             return (image, None)

        return StableDiffusionPipelineOutput(images=_snake_case					,						nsfw_content_detected=_snake_case)













import itertools
import math





def      lowerCAmelCase_ (       __a		)     ->		bool:







  """simple docstring"""





  if 1 < number < 4:
    # 2 and 3 are primes
    return True
  elif number < 2 or number % 2 == 0 or number % 3 == 0:
    # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
    return False

  # All primes number are in format of 6k +/- 1
  for i in range(5	,    int(math.sqrt(__a		) + 1		)	,    6		):
    if number % i == 0 or number % (i + 2) == 0:
      return False
  return True





def      lowerCAmelCase_ (       )     ->		str:







  """simple docstring"""





  lowerCamelCase__:      Optional[int]			  =2
  while True:
    if is_prime(__a		):
      yield num
    num += 1





def      lowerCAmelCase_ (       __a = 10001		)     ->		int:







  """simple docstring"""





  return next(itertools.islice(prime_generator()	,    nth - 1	,    __a		)		)


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

