"""simple docstring"""




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

import torch

from ...models import AutoencoderKL, TransformeraDModel
from ...schedulers import KarrasDiffusionSchedulers
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput
class 						__A							( SCREAMING_SNAKE_CASE_		):






     def __init__(		self				,     a__				,     a__				,     a__				,     a__ = None				,     ):
       super().__init__()
       self.register_modules(transformer=a__				,     vae=a__				,     scheduler=a__  )

       # create a imagenet -> id dictionary for easier use
       _lowerCAmelCase						:       Optional[int]  			=     {}
       if idalabel is not None:
         for key, value in idalabel.items():
           for label in value.split(""","""  ):
             _lowerCAmelCase						:       Any  			=     int(a__  )
         _lowerCAmelCase						:       List[Any]  			=     dict(sorted(self.labels.items()  )  )






     def     __A  (		self				,     a__  ):

       if not isinstance(a__				,     a__  ):
         _lowerCAmelCase						:       Union[str, Any]  			=     list(a__  )

       for l in label:
         if l not in self.labels:
           raise ValueError(
               F"{l} does not exist. Please make sure to select one of the following labels: \n {self.labels}."  )

       return [self.labels[l] for l in label]






     @torch.no_grad()
     def __call__(		self				,     a__				,     a__ = 4.0				,     a__ = None				,     a__ = 50				,     a__ = "pil"				,     a__ = True				,     ):
       _lowerCAmelCase						:       Optional[int]  			=     len(a__  )
       _lowerCAmelCase						:       Union[str, Any]  			=     self.transformer.config.sample_size
       _lowerCAmelCase						:       str  			=     self.transformer.config.in_channels

       _lowerCAmelCase						:       Any  			=     randn_tensor(
           shape=(batch_size, latent_channels, latent_size, latent_size)				,     generator=a__				,     device=self.device				,     dtype=self.transformer.dtype				,     )
       _lowerCAmelCase						:       Optional[int]  			=     torch.cat([latents] * 2  ) if guidance_scale > 1 else latents

       _lowerCAmelCase						:       Any  			=     torch.tensor(a__				,     device=self.device  ).reshape(-1  )
       _lowerCAmelCase						:       List[str]  			=     torch.tensor([1000] * batch_size				,     device=self.device  )
       _lowerCAmelCase						:       int  			=     torch.cat([class_labels, class_null]				,     0  ) if guidance_scale > 1 else class_labels

       # set step values
       self.scheduler.set_timesteps(a__  )

       for t in self.progress_bar(self.scheduler.timesteps  ):
         if guidance_scale > 1:
           _lowerCAmelCase						:       Dict  			=     latent_model_input[: len(a__  ) // 2]
           _lowerCAmelCase						:       Any  			=     torch.cat([half, half]				,     dim=0  )
         _lowerCAmelCase						:       Dict  			=     self.scheduler.scale_model_input(a__				,     a__  )

         _lowerCAmelCase						:       List[str]  			=     t
         if not torch.is_tensor(a__  ):
           # TODO: this requires sync between CPU and GPU. So try to pass timesteps as tensors if you can
           # This would be a good case for the `match` statement (Python 3.10+)
           _lowerCAmelCase						:       List[Any]  			=     latent_model_input.device.type == """mps"""
           if isinstance(a__				,     a__  ):
             _lowerCAmelCase						:       List[Any]  			=     torch.floataa if is_mps else torch.floataa
           else:
             _lowerCAmelCase						:       Tuple  			=     torch.intaa if is_mps else torch.intaa
           _lowerCAmelCase						:       Union[str, Any]  			=     torch.tensor([timesteps]				,     dtype=a__				,     device=latent_model_input.device  )
         elif len(timesteps.shape  ) == 0:
           _lowerCAmelCase						:       Any  			=     timesteps[None].to(latent_model_input.device  )
         # broadcast to batch dimension in a way that's compatible with ONNX/Core ML
         _lowerCAmelCase						:       Union[str, Any]  			=     timesteps.expand(latent_model_input.shape[0]  )
         # predict noise model_output
         _lowerCAmelCase						:       str  			=     self.transformer(
             a__				,     timestep=a__				,     class_labels=a__  ).sample

         # perform guidance
         if guidance_scale > 1:
           _lowerCAmelCase			,	_lowerCAmelCase						:       Any  			=     noise_pred[:, :latent_channels], noise_pred[:, latent_channels:]
           _lowerCAmelCase			,	_lowerCAmelCase						:       List[str]  			=     torch.split(a__				,     len(a__  ) // 2				,     dim=0  )

           _lowerCAmelCase						:       Union[str, Any]  			=     uncond_eps + guidance_scale * (cond_eps - uncond_eps)
           _lowerCAmelCase						:       Any  			=     torch.cat([half_eps, half_eps]				,     dim=0  )

           _lowerCAmelCase						:       List[Any]  			=     torch.cat([eps, rest]				,     dim=1  )

         # learned sigma
         if self.transformer.config.out_channels // 2 == latent_channels:
           _lowerCAmelCase			,	_lowerCAmelCase						:       str  			=     torch.split(a__				,     a__				,     dim=1  )
         else:
           _lowerCAmelCase						:       Any  			=     noise_pred

         # compute previous image: x_t -> x_t-1
         _lowerCAmelCase						:       str  			=     self.scheduler.step(a__				,     a__				,     a__  ).prev_sample

       if guidance_scale > 1:
         _lowerCAmelCase			,	_lowerCAmelCase						:       Any  			=     latent_model_input.chunk(2				,     dim=0  )
       else:
         _lowerCAmelCase						:       List[Any]  			=     latent_model_input

       _lowerCAmelCase						:       Union[str, Any]  			=     1 / self.vae.config.scaling_factor * latents
       _lowerCAmelCase						:       Optional[Any]  			=     self.vae.decode(a__  ).sample

       _lowerCAmelCase						:       Optional[int]  			=     (samples / 2 + 0.5).clamp(0				,     1  )

       # we always cast to float32 as this does not cause significant overhead and is compatible with bfloat16
       _lowerCAmelCase						:       List[str]  			=     samples.cpu().permute(0				,     2				,     3				,     1  ).float().numpy()

       if output_type == "pil":
         _lowerCAmelCase						:       Union[str, Any]  			=     self.numpy_to_pil(a__  )

       if not return_dict:
         return (samples,)

       return ImagePipelineOutput(images=a__  )





"""simple docstring"""




def 							SCREAMING_SNAKE_CASE     (			_lowerCamelCase						:       int = 50	)       ->      int:
  _lowerCAmelCase						:       int  			=     [1] * (length + 1)

  for row_length in range(3			,length + 1	):
    for block_length in range(3			,row_length + 1	):
      for block_start in range(row_length - block_length	):
        ways_number[row_length] += ways_number[
            row_length - block_start - block_length - 1
        ]

      ways_number[row_length] += 1

  return ways_number[length]


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




