

__snake_case				:      Tuple   		=			range(2, 20 + 1)
__snake_case				:      Any   		=			[10**k for k in range(ks[-1] + 1)]
__snake_case				:      Union[str, Any]   		=			{}


def 					_UpperCAmelCase				(						a__  ,	a__  ,	a__  ,	a__):

			'''simple docstring'''



			a_						:						Tuple 							= sum(a_i[j] for j in range(_snake_case  ,	len(_snake_case)))
			a_						:						Tuple 							= sum(a_i[j] * base[j] for j in range(min(len(_snake_case)  ,	_snake_case)))

			a_							,					a_						:						Optional[Any] 							= 0, 0
			a_						:						int 							= n - i

			a_						:						Tuple 							= memo.get(_snake_case)

			if sub_memo is not None:
						a_						:						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
									a_						:						Optional[int] 							= -1
									for _k in range(len(_snake_case) - 1  ,	-1  ,	-1):
												if jumps[_k][2] <= k and jumps[_k][1] <= max_dn:
															a_						:						Tuple 							= _k
															break

									if max_jump >= 0:
												a_							,					a_							,					a_						:						str 							= jumps[max_jump]
												# since the difference between jumps is cached, add c
												a_						:						List[Any] 							= diff + c
												for j in range(min(_snake_case  ,	len(_snake_case))):
															a_							,					a_						:						Tuple 							= divmod(_snake_case  ,	1_0)
												if new_c > 0:
															add(_snake_case  ,	_snake_case  ,	_snake_case)

						else:
									a_						:						Optional[int] 							= []
			else:
						a_						:						Any 							= {c: []}
						a_						:						str 							= sub_memo

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

			if k > ks[0]:
						while True:
									# keep doing smaller jumps
									a_							,					a_						:						List[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
						a_							,					a_						:						Tuple 							= compute(_snake_case  ,	_snake_case  ,	i + dn  ,	_snake_case)
						diff += _diff
						dn += terms_jumped

			a_						:						List[str] 							= sub_memo[c]

			# keep jumps sorted by # of terms skipped
			a_						:						List[Any] 							= 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 					_UpperCAmelCase				(						a__  ,	a__  ,	a__  ,	a__):

			'''simple docstring'''



			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)
			a_						:						Union[str, Any] 							= i
			a_							,					a_							,					a_						:						str 							= 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
						a_						:						Optional[Any] 							= ds_c + ds_b
						diff += addend
						a_						:						str 							= 0
						for j in range(_snake_case):
									a_						:						int 							= a_i[j] + addend
									a_							,					a_						:						List[Any] 							= divmod(_snake_case  ,	1_0)

									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 					_UpperCAmelCase				(						a__  ,	a__  ,	a__):

			'''simple docstring'''



			for j in range(_snake_case  ,	len(_snake_case)):
						a_						:						int 							= digits[j] + addend
						if s >= 1_0:
									a_							,					a_						:						List[str] 							= divmod(_snake_case  ,	1_0)
									a_						:						str 							= addend // 1_0 + quotient
						else:
									a_						:						Tuple 							= s
									a_						:						Dict 							= addend // 1_0

						if addend == 0:
									break

			while addend > 0:
						a_							,					a_						:						Tuple 							= divmod(_snake_case  ,	1_0)
						digits.append(_snake_case)


def 					_UpperCAmelCase				(						a__ = 1_0**1_5):

			'''simple docstring'''



			a_						:						Dict 							= [1]
			a_						:						Any 							= 1
			a_						:						Optional[int] 							= 0
			while True:
						a_							,					a_						:						Optional[int] 							= next_term(_snake_case  ,	2_0  ,	i + dn  ,	_snake_case)
						dn += terms_jumped
						if dn == n - i:
									break

			a_						:						str 							= 0
			for j in range(len(_snake_case)):
						a_n += digits[j] * 1_0**j
			return a_n


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










import unittest

import numpy as np
import torch

from diffusers import ScoreSdeVePipeline, ScoreSdeVeScheduler, UNetaDModel
from diffusers.utils.testing_utils import enable_full_determinism, require_torch, slow, torch_device


enable_full_determinism()






class 					SCREAMING_SNAKE_CASE_  (       unittest.TestCase ):
       """simple docstring"""


       @property
       def 				UpperCamelCase__						(				self	:Optional[int]):



          """simple docstring"""

          torch.manual_seed(0)
          _lowercase              =UNetaDModel(
              block_out_channels=(32, 64),      layers_per_block=2,      sample_size=32,      in_channels=3,      out_channels=3,      down_block_types=('DownBlock2D', 'AttnDownBlock2D'),      up_block_types=('AttnUpBlock2D', 'UpBlock2D'),      )
          return model





       def 				UpperCamelCase__						(				self	:str):



          """simple docstring"""

          _lowercase              =self.dummy_uncond_unet
          _lowercase              =ScoreSdeVeScheduler()

          _lowercase              =ScoreSdeVePipeline(unet=snake_case,      scheduler=snake_case)
          sde_ve.to(snake_case)
          sde_ve.set_progress_bar_config(disable=snake_case)

          _lowercase              =torch.manual_seed(0)
          _lowercase              =sde_ve(num_inference_steps=2,      output_type='numpy',      generator=snake_case).images

          _lowercase              =torch.manual_seed(0)
          _lowercase              =sde_ve(num_inference_steps=2,      output_type='numpy',      generator=snake_case,      return_dict=snake_case)[
              0
          ]

          _lowercase              =image[0, -3:, -3:, -1]
          _lowercase              =image_from_tuple[0, -3:, -3:, -1]

          assert image.shape == (1, 32, 32, 3)
          _lowercase              =np.array([0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0])

          assert np.abs(image_slice.flatten() - expected_slice).max() < 1e-2
          assert np.abs(image_from_tuple_slice.flatten() - expected_slice).max() < 1e-2






@slow
@require_torch
class 					SCREAMING_SNAKE_CASE_  (       unittest.TestCase ):
       """simple docstring"""


       def 				UpperCamelCase__						(				self	:int):



          """simple docstring"""

          _lowercase              ='google/ncsnpp-church-256'
          _lowercase              =UNetaDModel.from_pretrained(snake_case)

          _lowercase              =ScoreSdeVeScheduler.from_pretrained(snake_case)

          _lowercase              =ScoreSdeVePipeline(unet=snake_case,      scheduler=snake_case)
          sde_ve.to(snake_case)
          sde_ve.set_progress_bar_config(disable=snake_case)

          _lowercase              =torch.manual_seed(0)
          _lowercase              =sde_ve(num_inference_steps=10,      output_type='numpy',      generator=snake_case).images

          _lowercase              =image[0, -3:, -3:, -1]

          assert image.shape == (1, 256, 256, 3)

          _lowercase              =np.array([0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0])

          assert np.abs(image_slice.flatten() - expected_slice).max() < 1e-2


