





"""simple docstring"""




import types
from typing import List, Optional, Tuple, Union

import torch
from transformers import CLIPTextModelWithProjection, CLIPTokenizer
from transformers.models.clip.modeling_clip import CLIPTextModelOutput

from diffusers.models import PriorTransformer
from diffusers.pipelines import DiffusionPipeline, StableDiffusionImageVariationPipeline
from diffusers.schedulers import UnCLIPScheduler
from diffusers.utils import logging, randn_tensor


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





def 			a_							(				self			,		_lowercase			,		_lowercase			,		_lowercase			,		_lowercase  ):
						_UpperCamelCase     :   Optional[int]      =       image.to(device=_lowercase  )
						_UpperCamelCase     :   int      =       image  # take image as image_embeddings
						_UpperCamelCase     :   Optional[Any]      =       image_embeddings.unsqueeze(1  )

						# duplicate image embeddings for each generation per prompt, using mps friendly method
						_UpperCamelCase  ,				_UpperCamelCase  ,				_UpperCamelCase     :   str      =       image_embeddings.shape
						_UpperCamelCase     :   List[Any]      =       image_embeddings.repeat(1			,		_lowercase			,		1  )
						_UpperCamelCase     :   Optional[Any]      =       image_embeddings.view(bs_embed * num_images_per_prompt			,		_lowercase			,		-1  )

						if do_classifier_free_guidance:
												_UpperCamelCase     :   Dict      =       torch.zeros_like(_lowercase  )

												# 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     :   Any      =       torch.cat([uncond_embeddings, image_embeddings]  )

						return image_embeddings






class 					_a		( _lowerCAmelCase							):






				def __init__(					self						:       str,					lowerCAmelCase__						:       PriorTransformer,					lowerCAmelCase__						:       CLIPTokenizer,					lowerCAmelCase__						:       CLIPTextModelWithProjection,					lowerCAmelCase__						:       UnCLIPScheduler,					lowerCAmelCase__						:       Optional[dict] = None,					)      -> int:




										'''simple docstring'''



										super().__init__()

										_UpperCamelCase     :   Any      =       {'''image_encoder''': None} if decoder_pipe_kwargs is None else decoder_pipe_kwargs

										_UpperCamelCase     :   Union[str, Any]      =       decoder_pipe_kwargs.get('''torch_dtype''',					lowerCAmelCase__				) or prior.dtype

										_UpperCamelCase     :   Dict      =       StableDiffusionImageVariationPipeline.from_pretrained(
										    '''lambdalabs/sd-image-variations-diffusers''',					**lowerCAmelCase__				)

										# replace `_encode_image` method
										_UpperCamelCase     :   Optional[Any]      =       types.MethodType(_encode_image,					self.decoder_pipe				)

										self.register_modules(
										    prior=lowerCAmelCase__,					tokenizer=lowerCAmelCase__,					text_encoder=lowerCAmelCase__,					prior_scheduler=lowerCAmelCase__,					)






				def 							snake_case      (					self						:       str,					lowerCAmelCase__						:       Optional[Any],					lowerCAmelCase__						:       Optional[Any],					lowerCAmelCase__						:       str,					lowerCAmelCase__						:       List[Any],					lowerCAmelCase__						:       Optional[Union[CLIPTextModelOutput, Tuple]] = None,					lowerCAmelCase__						:       Optional[torch.Tensor] = None,					)      -> Tuple:




										'''simple docstring'''



										if text_model_output is None:
																_UpperCamelCase     :   List[Any]      =       len(lowerCAmelCase__				) if isinstance(lowerCAmelCase__,					lowerCAmelCase__				) else 1
																# get prompt text embeddings
																_UpperCamelCase     :   Any      =       self.tokenizer(
																    lowerCAmelCase__,					padding='''max_length''',					max_length=self.tokenizer.model_max_length,					return_tensors='''pt''',					)
																_UpperCamelCase     :   List[str]      =       text_inputs.input_ids
																_UpperCamelCase     :   List[str]      =       text_inputs.attention_mask.bool().to(lowerCAmelCase__				)

																if text_input_ids.shape[-1] > self.tokenizer.model_max_length:
																						_UpperCamelCase     :   str      =       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}"""				)
																						_UpperCamelCase     :   Optional[Any]      =       text_input_ids[:, : self.tokenizer.model_max_length]

																_UpperCamelCase     :   Dict      =       self.text_encoder(text_input_ids.to(lowerCAmelCase__				)				)

																_UpperCamelCase     :   Optional[int]      =       text_encoder_output.text_embeds
																_UpperCamelCase     :   List[Any]      =       text_encoder_output.last_hidden_state

										else:
																_UpperCamelCase     :   Any      =       text_model_output[0].shape[0]
																_UpperCamelCase  ,				_UpperCamelCase     :   Any      =       text_model_output[0], text_model_output[1]
																_UpperCamelCase     :   Optional[Any]      =       text_attention_mask

										_UpperCamelCase     :   Optional[Any]      =       text_embeddings.repeat_interleave(lowerCAmelCase__,					dim=0				)
										_UpperCamelCase     :   Dict      =       text_encoder_hidden_states.repeat_interleave(lowerCAmelCase__,					dim=0				)
										_UpperCamelCase     :   int      =       text_mask.repeat_interleave(lowerCAmelCase__,					dim=0				)

										if do_classifier_free_guidance:
																_UpperCamelCase     :   int      =       [''''''] * batch_size

																_UpperCamelCase     :   Tuple      =       self.tokenizer(
																    lowerCAmelCase__,					padding='''max_length''',					max_length=self.tokenizer.model_max_length,					truncation=lowerCAmelCase__,					return_tensors='''pt''',					)
																_UpperCamelCase     :   Tuple      =       uncond_input.attention_mask.bool().to(lowerCAmelCase__				)
																_UpperCamelCase     :   str      =       self.text_encoder(uncond_input.input_ids.to(lowerCAmelCase__				)				)

																_UpperCamelCase     :   Tuple      =       uncond_embeddings_text_encoder_output.text_embeds
																_UpperCamelCase     :   List[Any]      =       uncond_embeddings_text_encoder_output.last_hidden_state

																# duplicate unconditional embeddings for each generation per prompt, using mps friendly method

																_UpperCamelCase     :   Dict      =       uncond_embeddings.shape[1]
																_UpperCamelCase     :   Optional[Any]      =       uncond_embeddings.repeat(1,					lowerCAmelCase__				)
																_UpperCamelCase     :   Union[str, Any]      =       uncond_embeddings.view(batch_size * num_images_per_prompt,					lowerCAmelCase__				)

																_UpperCamelCase     :   Optional[Any]      =       uncond_text_encoder_hidden_states.shape[1]
																_UpperCamelCase     :   List[Any]      =       uncond_text_encoder_hidden_states.repeat(1,					lowerCAmelCase__,					1				)
																_UpperCamelCase     :   List[str]      =       uncond_text_encoder_hidden_states.view(
																    batch_size * num_images_per_prompt,					lowerCAmelCase__,					-1				)
																_UpperCamelCase     :   Any      =       uncond_text_mask.repeat_interleave(lowerCAmelCase__,					dim=0				)

																# done duplicates

																# 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     :   Any      =       torch.cat([uncond_embeddings, text_embeddings]				)
																_UpperCamelCase     :   Dict      =       torch.cat([uncond_text_encoder_hidden_states, text_encoder_hidden_states]				)

																_UpperCamelCase     :   Optional[Any]      =       torch.cat([uncond_text_mask, text_mask]				)

										return text_embeddings, text_encoder_hidden_states, text_mask






				@property
				def 							snake_case      (					self						:       int				)      -> Optional[int]:




										'''simple docstring'''



										if self.device != torch.device('''meta'''				) or not hasattr(self.prior,					'''_hf_hook'''				):
																return self.device
										for module in self.prior.modules():
																if (
																    hasattr(lowerCAmelCase__,					'''_hf_hook'''				)
																    and hasattr(module._hf_hook,					'''execution_device'''				)
																    and module._hf_hook.execution_device is not None
																):
																						return torch.device(module._hf_hook.execution_device				)
										return self.device






				def 							snake_case      (					self						:       Tuple,					lowerCAmelCase__						:       List[str],					lowerCAmelCase__						:       Dict,					lowerCAmelCase__						:       Optional[int],					lowerCAmelCase__						:       Dict,					lowerCAmelCase__						:       Optional[Any],					lowerCAmelCase__						:       Optional[int]				)      -> int:




										'''simple docstring'''



										if latents is None:
																_UpperCamelCase     :   Union[str, Any]      =       randn_tensor(lowerCAmelCase__,					generator=lowerCAmelCase__,					device=lowerCAmelCase__,					dtype=lowerCAmelCase__				)
										else:
																if latents.shape != shape:
																						raise ValueError(f"""Unexpected latents shape, got {latents.shape}, expected {shape}"""				)
																_UpperCamelCase     :   Union[str, Any]      =       latents.to(lowerCAmelCase__				)

										_UpperCamelCase     :   List[Any]      =       latents * scheduler.init_noise_sigma
										return latents






				def 							snake_case      (					self						:       Dict,					lowerCAmelCase__						:       Optional[Union[str, torch.device]] = None				)      -> Optional[Any]:




										'''simple docstring'''



										self.decoder_pipe.to(lowerCAmelCase__				)
										super().to(lowerCAmelCase__				)






				@torch.no_grad()
				def __call__(					self						:       Tuple,					lowerCAmelCase__						:       Optional[Union[str, List[str]]] = None,					lowerCAmelCase__						:       Optional[int] = None,					lowerCAmelCase__						:       Optional[int] = None,					lowerCAmelCase__						:       int = 1,					lowerCAmelCase__						:       int = 2_5,					lowerCAmelCase__						:       Optional[torch.Generator] = None,					lowerCAmelCase__						:       Optional[torch.FloatTensor] = None,					lowerCAmelCase__						:       Optional[Union[CLIPTextModelOutput, Tuple]] = None,					lowerCAmelCase__						:       Optional[torch.Tensor] = None,					lowerCAmelCase__						:       float = 4.0,					lowerCAmelCase__						:       float = 8.0,					lowerCAmelCase__						:       int = 5_0,					lowerCAmelCase__						:       Optional[int] = 1,					lowerCAmelCase__						:       float = 0.0,					lowerCAmelCase__						:       Optional[str] = "pil",					lowerCAmelCase__						:       bool = True,					)      -> Tuple:




										'''simple docstring'''



										if prompt is not None:
																if isinstance(lowerCAmelCase__,					lowerCAmelCase__				):
																						_UpperCamelCase     :   Optional[int]      =       1
																elif isinstance(lowerCAmelCase__,					lowerCAmelCase__				):
																						_UpperCamelCase     :   List[Any]      =       len(lowerCAmelCase__				)
																else:
																						raise ValueError(f"""`prompt` has to be of type `str` or `list` but is {type(lowerCAmelCase__				)}"""				)
										else:
																_UpperCamelCase     :   Any      =       text_model_output[0].shape[0]

										_UpperCamelCase     :   Tuple      =       self._execution_device

										_UpperCamelCase     :   Optional[int]      =       batch_size * num_images_per_prompt

										_UpperCamelCase     :   List[Any]      =       prior_guidance_scale > 1.0 or decoder_guidance_scale > 1.0

										_UpperCamelCase  ,				_UpperCamelCase  ,				_UpperCamelCase     :   Optional[Any]      =       self._encode_prompt(
										    lowerCAmelCase__,					lowerCAmelCase__,					lowerCAmelCase__,					lowerCAmelCase__,					lowerCAmelCase__,					lowerCAmelCase__				)

										# prior

										self.prior_scheduler.set_timesteps(lowerCAmelCase__,					device=lowerCAmelCase__				)
										_UpperCamelCase     :   Tuple      =       self.prior_scheduler.timesteps

										_UpperCamelCase     :   str      =       self.prior.config.embedding_dim

										_UpperCamelCase     :   Dict      =       self.prepare_latents(
										    (batch_size, embedding_dim),					text_embeddings.dtype,					lowerCAmelCase__,					lowerCAmelCase__,					lowerCAmelCase__,					self.prior_scheduler,					)

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

																_UpperCamelCase     :   Any      =       self.prior(
																    lowerCAmelCase__,					timestep=lowerCAmelCase__,					proj_embedding=lowerCAmelCase__,					encoder_hidden_states=lowerCAmelCase__,					attention_mask=lowerCAmelCase__,					).predicted_image_embedding

																if do_classifier_free_guidance:
																						_UpperCamelCase  ,				_UpperCamelCase     :   Any      =       predicted_image_embedding.chunk(2				)
																						_UpperCamelCase     :   List[str]      =       predicted_image_embedding_uncond + prior_guidance_scale * (
																						    predicted_image_embedding_text - predicted_image_embedding_uncond
																						)

																if i + 1 == prior_timesteps_tensor.shape[0]:
																						_UpperCamelCase     :   Union[str, Any]      =       None
																else:
																						_UpperCamelCase     :   Union[str, Any]      =       prior_timesteps_tensor[i + 1]

																_UpperCamelCase     :   Dict      =       self.prior_scheduler.step(
																    lowerCAmelCase__,					timestep=lowerCAmelCase__,					sample=lowerCAmelCase__,					generator=lowerCAmelCase__,					prev_timestep=lowerCAmelCase__,					).prev_sample

										_UpperCamelCase     :   str      =       self.prior.post_process_latents(lowerCAmelCase__				)

										_UpperCamelCase     :   List[Any]      =       prior_latents

										_UpperCamelCase     :   Tuple      =       self.decoder_pipe(
										    image=lowerCAmelCase__,					height=lowerCAmelCase__,					width=lowerCAmelCase__,					num_inference_steps=lowerCAmelCase__,					guidance_scale=lowerCAmelCase__,					generator=lowerCAmelCase__,					output_type=lowerCAmelCase__,					return_dict=lowerCAmelCase__,					num_images_per_prompt=lowerCAmelCase__,					eta=lowerCAmelCase__,					)
										return output







"""simple docstring"""


from math import factorial






def   a__			(					__lowercase  ,      __lowercase )						->						List[Any]:
				return factorial(__lowercase ) / (factorial(__lowercase ) * factorial(n - r ))






def   a__			(					)						->						List[str]:
				_A       	=      0

				for i in range(1  ,      101 ):
								for j in range(1  ,      i + 1 ):
												if combinations(__lowercase  ,      __lowercase ) > 1E6:
																total += 1
				return total


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