

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     a__  (    __UpperCamelCase	):
			"""simple docstring"""







			__lowerCamelCase       				=				42
			__lowerCamelCase       				=				42


			def __init__(			self					,					lowercase					,					lowercase				)     ->  Any:
							'''simple docstring'''






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


			@torch.no_grad()
			def __call__(			self					,					lowercase = 1					,					lowercase = 2000					,					lowercase = None					,					lowercase = "pil"					,					lowercase = True					,					**lowercase					,					)     ->  Union[ImagePipelineOutput, Tuple]:
							'''simple docstring'''






							A__						=	self.unet.config.sample_size
							A__						=	(batch_size, 3, img_size, img_size)

							A__						=	self.unet

							A__						=	randn_tensor(lowerCAmelCase__					,					generator=lowerCAmelCase__				) * self.scheduler.init_noise_sigma
							A__						=	sample.to(self.device				)

							self.scheduler.set_timesteps(lowerCAmelCase__				)
							self.scheduler.set_sigmas(lowerCAmelCase__				)

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

											# correction step
											for _ in range(self.scheduler.config.correct_steps				):
															A__						=	self.unet(lowerCAmelCase__					,					lowerCAmelCase__				).sample
															A__						=	self.scheduler.step_correct(lowerCAmelCase__					,					lowerCAmelCase__					,					generator=lowerCAmelCase__				).prev_sample

											# prediction step
											A__						=	model(lowerCAmelCase__					,					lowerCAmelCase__				).sample
											A__						=	self.scheduler.step_pred(lowerCAmelCase__					,					lowerCAmelCase__					,					lowerCAmelCase__					,					generator=lowerCAmelCase__				)

											A__						=	output.prev_sample, output.prev_sample_mean

							A__						=	sample_mean.clamp(0					,					1				)
							A__						=	sample.cpu().permute(0					,					2					,					3					,					1				).numpy()
							if output_type == "pil":
											A__						=	self.numpy_to_pil(lowerCAmelCase__				)

							if not return_dict:
											return (sample,)

							return ImagePipelineOutput(images=lowerCAmelCase__				)





__lowerCAmelCase		       =							range(2, 20 + 1)
__lowerCAmelCase		       =							[10**k for k in range(ks[-1] + 1)]
__lowerCAmelCase		       =							{}




def    snake_case_     (  snake_case			,							snake_case			,							snake_case			,							snake_case     )  ->				Optional[int]:
       lowercase__:   str  			=   sum(a_i[j] for j in range(snake_case			,							len(snake_case     )     )     )
       lowercase__:   Optional[int]  			=   sum(a_i[j] * base[j] for j in range(min(len(snake_case     )			,							snake_case     )     )     )

       lowercase__			,						lowercase__:   str  			=   0, 0
       lowercase__:   Tuple  			=   n - i

       lowercase__:   Dict  			=   memo.get(snake_case     )

       if sub_memo is not None:
              lowercase__:   Optional[Any]  			=   sub_memo.get(snake_case     )

              if jumps is not None and len(snake_case     ) > 0:
                     # find and make the largest jump without going over
                     lowercase__:   int  			=   -1
                     for _k in range(len(snake_case     ) - 1			,							-1			,							-1     ):
                            if jumps[_k][2] <= k and jumps[_k][1] <= max_dn:
                                   lowercase__:   Union[str, Any]  			=   _k
                                   break

                     if max_jump >= 0:
                            lowercase__			,						lowercase__			,						lowercase__:   Any  			=   jumps[max_jump]
                            # since the difference between jumps is cached, add c
                            lowercase__:   str  			=   diff + c
                            for j in range(min(snake_case			,							len(snake_case     )     )     ):
                                   lowercase__			,						lowercase__:   Dict  			=   divmod(snake_case			,							10     )
                            if new_c > 0:
                                   add(snake_case			,							snake_case			,							snake_case     )

              else:
                     lowercase__:   List[Any]  			=   []
       else:
              lowercase__:   Optional[Any]  			=   {c: []}
              lowercase__:   Union[str, Any]  			=   sub_memo

       if dn >= max_dn or c + diff >= base[k]:
              return diff, dn

       if k > ks[0]:
              while True:
                     # keep doing smaller jumps
                     lowercase__			,						lowercase__:   Union[str, Any]  			=   next_term(snake_case			,							k - 1			,							i + dn			,							snake_case     )
                     diff += _diff
                     dn += terms_jumped

                     if dn >= max_dn or c + diff >= base[k]:
                            break
       else:
              # would be too small a jump, just compute sequential terms instead
              lowercase__			,						lowercase__:   Dict  			=   compute(snake_case			,							snake_case			,							i + dn			,							snake_case     )
              diff += _diff
              dn += terms_jumped

       lowercase__:   Any  			=   sub_memo[c]

       # keep jumps sorted by # of terms skipped
       lowercase__:   str  			=   0
       while j < len(snake_case     ):
              if jumps[j][1] > dn:
                     break
              j += 1

       # cache the jump for this value digitsum(b) and c
       sub_memo[c].insert(snake_case			,							(diff, dn, k)     )
       return (diff, dn)




def    snake_case_     (  snake_case			,							snake_case			,							snake_case			,							snake_case     )  ->				str:
       if i >= n:
              return 0, i
       if k > len(snake_case     ):
              a_i.extend([0 for _ in range(k - len(snake_case     )     )]     )

       # note: a_i -> b * 10^k + c
       # ds_b -> digitsum(b)
       # ds_c -> digitsum(c)
       lowercase__:   List[Any]  			=   i
       lowercase__			,						lowercase__			,						lowercase__:   Any  			=   0, 0, 0
       for j in range(len(snake_case     )     ):
              if j >= k:
                     ds_b += a_i[j]
              else:
                     ds_c += a_i[j]

       while i < n:
              i += 1
              lowercase__:   str  			=   ds_c + ds_b
              diff += addend
              lowercase__:   List[str]  			=   0
              for j in range(snake_case     ):
                     lowercase__:   Any  			=   a_i[j] + addend
                     lowercase__			,						lowercase__:   List[Any]  			=   divmod(snake_case			,							10     )

                     ds_c += a_i[j]

              if addend > 0:
                     break

       if addend > 0:
              add(snake_case			,							snake_case			,							snake_case     )
       return diff, i - start_i




def    snake_case_     (  snake_case			,							snake_case			,							snake_case     )  ->				int:
       for j in range(snake_case			,							len(snake_case     )     ):
              lowercase__:   str  			=   digits[j] + addend
              if s >= 10:
                     lowercase__			,						lowercase__:   Any  			=   divmod(snake_case			,							10     )
                     lowercase__:   Any  			=   addend // 10 + quotient
              else:
                     lowercase__:   Union[str, Any]  			=   s
                     lowercase__:   Union[str, Any]  			=   addend // 10

              if addend == 0:
                     break

       while addend > 0:
              lowercase__			,						lowercase__:   Union[str, Any]  			=   divmod(snake_case			,							10     )
              digits.append(snake_case     )




def    snake_case_     (  snake_case = 10**15     )  ->				int:
       lowercase__:   Optional[Any]  			=   [1]
       lowercase__:   int  			=   1
       lowercase__:   Tuple  			=   0
       while True:
              lowercase__			,						lowercase__:   str  			=   next_term(snake_case			,							20			,							i + dn			,							snake_case     )
              dn += terms_jumped
              if dn == n - i:
                     break

       lowercase__:   Dict  			=   0
       for j in range(len(snake_case     )     ):
              a_n += digits[j] * 10**j
       return a_n


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


