


'''simple docstring'''



from functools import reduce

A__						:   Union[str, Any]				=    (
    """73167176531330624919225119674426574742355349194934"""
    """96983520312774506326239578318016984801869478851843"""
    """85861560789112949495459501737958331952853208805511"""
    """12540698747158523863050715693290963295227443043557"""
    """66896648950445244523161731856403098711121722383113"""
    """62229893423380308135336276614282806444486645238749"""
    """30358907296290491560440772390713810515859307960866"""
    """70172427121883998797908792274921901699720888093776"""
    """65727333001053367881220235421809751254540594752243"""
    """52584907711670556013604839586446706324415722155397"""
    """53697817977846174064955149290862569321978468622482"""
    """83972241375657056057490261407972968652414535100474"""
    """82166370484403199890008895243450658541227588666881"""
    """16427171479924442928230863465674813919123162824586"""
    """17866458359124566529476545682848912883142607690042"""
    """24219022671055626321111109370544217506941658960408"""
    """07198403850962455444362981230987879927244284909188"""
    """84580156166097919133875499200524063689912560717606"""
    """05886116467109405077541002256983155200055935729725"""
    """71636269561882670428252483600823257530420752963450"""
)



def      UpperCAmelCase__   (      UpperCAmelCase_       :							str = N				)	->						int:
     return max(
         # mypy cannot properly interpret reduce
         int(reduce(lambda UpperCAmelCase_ ,       UpperCAmelCase_				: str(int(UpperCAmelCase_				) * int(UpperCAmelCase_				)				) ,       n[i : i + 13]				)				)
         for i in range(len(UpperCAmelCase_				) - 12				)				)


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










from typing import List, Optional, Tuple, Union

import torch

from ...models import UNetaDModel
from ...schedulers import ScoreSdeVeScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput




class 							lowerCamelCase   (  _UpperCamelCase ):
	_lowerCAmelCase     :		UNetaDModel
	_lowerCAmelCase     :		ScoreSdeVeScheduler


	def __init__(    self				,     lowercase__				,     lowercase__):
							super().__init__()
							self.register_modules(unet=lowercase__				,     scheduler=lowercase__)


	@torch.no_grad()
	def __call__(    self				,     lowercase__ = 1				,     lowercase__ = 2_0_0_0				,     lowercase__ = None				,     lowercase__ = "pil"				,     lowercase__ = True				,     **lowercase__				,     ):
							__UpperCAmelCase			:							int	    =	self.unet.config.sample_size
							__UpperCAmelCase			:							Optional[int]	    =	(batch_size, 3, img_size, img_size)

							__UpperCAmelCase			:							int	    =	self.unet

							__UpperCAmelCase			:							Tuple	    =	randn_tensor(lowercase__				,     generator=lowercase__) * self.scheduler.init_noise_sigma
							__UpperCAmelCase			:							List[str]	    =	sample.to(self.device)

							self.scheduler.set_timesteps(lowercase__)
							self.scheduler.set_sigmas(lowercase__)

							for i, t in enumerate(self.progress_bar(self.scheduler.timesteps)):
													__UpperCAmelCase			:							List[str]	    =	self.scheduler.sigmas[i] * torch.ones(shape[0]				,     device=self.device)

													# correction step
													for _ in range(self.scheduler.config.correct_steps):
																			__UpperCAmelCase			:							int	    =	self.unet(lowercase__				,     lowercase__).sample
																			__UpperCAmelCase			:							str	    =	self.scheduler.step_correct(lowercase__				,     lowercase__				,     generator=lowercase__).prev_sample

													# prediction step
													__UpperCAmelCase			:							Tuple	    =	model(lowercase__				,     lowercase__).sample
													__UpperCAmelCase			:							Dict	    =	self.scheduler.step_pred(lowercase__				,     lowercase__				,     lowercase__				,     generator=lowercase__)

													__UpperCAmelCase    ,      __UpperCAmelCase			:							Optional[Any]	    =	output.prev_sample, output.prev_sample_mean

							__UpperCAmelCase			:							List[str]	    =	sample_mean.clamp(0				,     1)
							__UpperCAmelCase			:							Union[str, Any]	    =	sample.cpu().permute(0				,     2				,     3				,     1).numpy()
							if output_type == "pil":
													__UpperCAmelCase			:							List[Any]	    =	self.numpy_to_pil(lowercase__)

							if not return_dict:
													return (sample,)

							return ImagePipelineOutput(images=lowercase__)

