





def 				SCREAMING_SNAKE_CASE__							(       UpperCamelCase__:							int = 100    ):
		SCREAMING_SNAKE_CASE__			=      (n * (n + 1) // 2) ** 2
		SCREAMING_SNAKE_CASE__			=      n * (n + 1) * (2 * n + 1) // 6
		return sum_cubes - sum_squares


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






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

import numpy as np
import PIL
import torch

from ...models import UNetaDModel
from ...schedulers import RePaintScheduler
from ...utils import PIL_INTERPOLATION, logging, randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput


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






def 				SCREAMING_SNAKE_CASE__							(       UpperCamelCase__:							Union[List, PIL.Image.Image, torch.Tensor]    ):
		warnings.warn(
		    """The preprocess method is deprecated and will be removed in a future version. Please"""
		    """ use VaeImageProcessor.preprocess instead"""					,   UpperCamelCase__					,   )
		if isinstance(UpperCamelCase__					,   torch.Tensor    ):
				return image
		elif isinstance(UpperCamelCase__					,   PIL.Image.Image    ):
				SCREAMING_SNAKE_CASE__			=      [image]

		if isinstance(image[0]					,   PIL.Image.Image    ):
				SCREAMING_SNAKE_CASE__	,						SCREAMING_SNAKE_CASE__			=      image[0].size
				SCREAMING_SNAKE_CASE__	,						SCREAMING_SNAKE_CASE__			=      (x - x % 8 for x in (w, h))  # resize to integer multiple of 8

				SCREAMING_SNAKE_CASE__			=      [np.array(i.resize((w, h)					,   resample=PIL_INTERPOLATION["""lanczos"""]    )    )[None, :] for i in image]
				SCREAMING_SNAKE_CASE__			=      np.concatenate(UpperCamelCase__					,   axis=0    )
				SCREAMING_SNAKE_CASE__			=      np.array(UpperCamelCase__    ).astype(np.floataa    ) / 2_5_5.0
				SCREAMING_SNAKE_CASE__			=      image.transpose(0					,   3					,   1					,   2    )
				SCREAMING_SNAKE_CASE__			=      2.0 * image - 1.0
				SCREAMING_SNAKE_CASE__			=      torch.from_numpy(UpperCamelCase__    )
		elif isinstance(image[0]					,   torch.Tensor    ):
				SCREAMING_SNAKE_CASE__			=      torch.cat(UpperCamelCase__					,   dim=0    )
		return image






def 				SCREAMING_SNAKE_CASE__							(       UpperCamelCase__:							Union[List, PIL.Image.Image, torch.Tensor]    ):
		if isinstance(UpperCamelCase__					,   torch.Tensor    ):
				return mask
		elif isinstance(UpperCamelCase__					,   PIL.Image.Image    ):
				SCREAMING_SNAKE_CASE__			=      [mask]

		if isinstance(mask[0]					,   PIL.Image.Image    ):
				SCREAMING_SNAKE_CASE__	,						SCREAMING_SNAKE_CASE__			=      mask[0].size
				SCREAMING_SNAKE_CASE__	,						SCREAMING_SNAKE_CASE__			=      (x - x % 32 for x in (w, h))  # resize to integer multiple of 32
				SCREAMING_SNAKE_CASE__			=      [np.array(m.convert("""L"""    ).resize((w, h)					,   resample=PIL_INTERPOLATION["""nearest"""]    )    )[None, :] for m in mask]
				SCREAMING_SNAKE_CASE__			=      np.concatenate(UpperCamelCase__					,   axis=0    )
				SCREAMING_SNAKE_CASE__			=      mask.astype(np.floataa    ) / 2_5_5.0
				SCREAMING_SNAKE_CASE__			=      0
				SCREAMING_SNAKE_CASE__			=      1
				SCREAMING_SNAKE_CASE__			=      torch.from_numpy(UpperCamelCase__    )
		elif isinstance(mask[0]					,   torch.Tensor    ):
				SCREAMING_SNAKE_CASE__			=      torch.cat(UpperCamelCase__					,   dim=0    )
		return mask




class   UpperCamelCase_       (     UpperCamelCase__    ):
							lowerCamelCase_           =					42
							lowerCamelCase_           =					42


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



									"""simple docstring"""



									super().__init__()
									self.register_modules(unet=__A							,				scheduler=__A		)


							@torch.no_grad()
							def __call__(							self    :str							,				__A    :Union[torch.Tensor, PIL.Image.Image]							,				__A    :Union[torch.Tensor, PIL.Image.Image]							,				__A    :int = 250							,				__A    :float = 0.0							,				__A    :int = 10							,				__A    :int = 10							,				__A    :Optional[Union[torch.Generator, List[torch.Generator]]] = None							,				__A    :Optional[str] = "pil"							,				__A    :bool = True							,				)   ->   Union[ImagePipelineOutput, Tuple]:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__			=      image

									SCREAMING_SNAKE_CASE__			=      _preprocess_image(__A		)
									SCREAMING_SNAKE_CASE__			=      original_image.to(device=self.device							,				dtype=self.unet.dtype		)
									SCREAMING_SNAKE_CASE__			=      _preprocess_mask(__A		)
									SCREAMING_SNAKE_CASE__			=      mask_image.to(device=self.device							,				dtype=self.unet.dtype		)

									SCREAMING_SNAKE_CASE__			=      original_image.shape[0]

									# sample gaussian noise to begin the loop
									if isinstance(__A							,				__A		) and len(__A		) != batch_size:
											raise ValueError(
											    f'''You have passed a list of generators of length {len(__A		)}, but requested an effective batch'''
											    f''' size of {batch_size}. Make sure the batch size matches the length of the generators.'''		)

									SCREAMING_SNAKE_CASE__			=      original_image.shape
									SCREAMING_SNAKE_CASE__			=      randn_tensor(__A							,				generator=__A							,				device=self.device							,				dtype=self.unet.dtype		)

									# set step values
									self.scheduler.set_timesteps(__A							,				__A							,				__A							,				self.device		)
									SCREAMING_SNAKE_CASE__			=      eta

									SCREAMING_SNAKE_CASE__			=      self.scheduler.timesteps[0] + 1
									SCREAMING_SNAKE_CASE__			=      generator[0] if isinstance(__A							,				__A		) else generator
									for i, t in enumerate(self.progress_bar(self.scheduler.timesteps		)		):
											if t < t_last:
													# predict the noise residual
													SCREAMING_SNAKE_CASE__			=      self.unet(__A							,				__A		).sample
													# compute previous image: x_t -> x_t-1
													SCREAMING_SNAKE_CASE__			=      self.scheduler.step(__A							,				__A							,				__A							,				__A							,				__A							,				__A		).prev_sample

											else:
													# compute the reverse: x_t-1 -> x_t
													SCREAMING_SNAKE_CASE__			=      self.scheduler.undo_step(__A							,				__A							,				__A		)
											SCREAMING_SNAKE_CASE__			=      t

									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(__A		)

									if not return_dict:
											return (image,)

									return ImagePipelineOutput(images=__A		)