


'''simple docstring'''
# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

import math
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin, SchedulerOutput
@dataclass
class      lowercase			(							A__      ):

		"""simple docstring"""

		_a									=       42
		_a									=       42



class      lowercase			(							A__			,	A__      ):

		"""simple docstring"""

		_a									=       1




		@register_to_config
		def __init__(	self					,     UpperCamelCase_ = 2000					,     UpperCamelCase_ = 0.15					,     UpperCamelCase_ = 0.01					,     UpperCamelCase_ = 1348.0					,     UpperCamelCase_ = 1e-5					,     UpperCamelCase_ = 1					,     ):

							'''simple docstring'''


							UpperCamelCase__     :int							      =				sigma_max

							# setable values
							UpperCamelCase__     :Any							      =				None

							self.set_sigmas(UpperCamelCase_					,     UpperCamelCase_					,     UpperCamelCase_					,     UpperCamelCase_							)




		def 					lowerCAmelCase__       (	self					,     UpperCamelCase_					,     UpperCamelCase_ = None							):

							'''simple docstring'''


							return sample




		def 					lowerCAmelCase__       (	self					,     UpperCamelCase_					,     UpperCamelCase_ = None					,     UpperCamelCase_ = None							):

							'''simple docstring'''


							UpperCamelCase__     :str							      =				sampling_eps if sampling_eps is not None else self.config.sampling_eps

							UpperCamelCase__     :Dict							      =				torch.linspace(1					,     UpperCamelCase_					,     UpperCamelCase_					,     device=UpperCamelCase_							)




		def 					lowerCAmelCase__       (	self					,     UpperCamelCase_					,     UpperCamelCase_ = None					,     UpperCamelCase_ = None					,     UpperCamelCase_ = None							):

							'''simple docstring'''


							UpperCamelCase__     :int							      =				sigma_min if sigma_min is not None else self.config.sigma_min
							UpperCamelCase__     :int							      =				sigma_max if sigma_max is not None else self.config.sigma_max
							UpperCamelCase__     :Dict							      =				sampling_eps if sampling_eps is not None else self.config.sampling_eps
							if self.timesteps is None:
												self.set_timesteps(UpperCamelCase_					,     UpperCamelCase_							)

							UpperCamelCase__     :Optional[Any]							      =				sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
							UpperCamelCase__     :Optional[Any]							      =				torch.exp(torch.linspace(math.log(UpperCamelCase_							)					,     math.log(UpperCamelCase_							)					,     UpperCamelCase_							)							)
							UpperCamelCase__     :Dict							      =				torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps]							)




		def 					lowerCAmelCase__       (	self					,     UpperCamelCase_					,     UpperCamelCase_							):

							'''simple docstring'''


							return torch.where(
							    timesteps == 0					,     torch.zeros_like(t.to(timesteps.device							)							)					,     self.discrete_sigmas[timesteps - 1].to(timesteps.device							)					,     )




		def 					lowerCAmelCase__       (	self					,     UpperCamelCase_					,     UpperCamelCase_					,     UpperCamelCase_					,     UpperCamelCase_ = None					,     UpperCamelCase_ = True					,     ):

							'''simple docstring'''


							if self.timesteps is None:
												raise ValueError(
												    '''`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler'''							)

							UpperCamelCase__     :Dict							      =				timestep * torch.ones(
							    sample.shape[0]					,     device=sample.device							)  # torch.repeat_interleave(timestep, sample.shape[0])
							UpperCamelCase__     :List[Any]							      =				(timestep * (len(self.timesteps							) - 1)).long()

							# mps requires indices to be in the same device, so we use cpu as is the default with cuda
							UpperCamelCase__     :Dict							      =				timesteps.to(self.discrete_sigmas.device							)

							UpperCamelCase__     :int							      =				self.discrete_sigmas[timesteps].to(sample.device							)
							UpperCamelCase__     :List[str]							      =				self.get_adjacent_sigma(UpperCamelCase_					,     UpperCamelCase_							).to(sample.device							)
							UpperCamelCase__     :int							      =				torch.zeros_like(UpperCamelCase_							)
							UpperCamelCase__     :int							      =				(sigma**2 - adjacent_sigma**2) ** 0.5

							# equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
							# also equation 47 shows the analog from SDE models to ancestral sampling methods
							UpperCamelCase__     :Tuple							      =				diffusion.flatten()
							while len(diffusion.shape							) < len(sample.shape							):
												UpperCamelCase__     :Tuple							      =				diffusion.unsqueeze(-1							)
							UpperCamelCase__     :List[str]							      =				drift - diffusion**2 * model_output

							#  equation 6: sample noise for the diffusion term of
							UpperCamelCase__     :List[str]							      =				randn_tensor(
							    sample.shape					,     layout=sample.layout					,     generator=UpperCamelCase_					,     device=sample.device					,     dtype=sample.dtype							)
							UpperCamelCase__     :Union[str, Any]							      =				sample - drift  # subtract because `dt` is a small negative timestep
							# TODO is the variable diffusion the correct scaling term for the noise?
							UpperCamelCase__     :int							      =				prev_sample_mean + diffusion * noise  # add impact of diffusion field g

							if not return_dict:
												return (prev_sample, prev_sample_mean)

							return SdeVeOutput(prev_sample=UpperCamelCase_					,     prev_sample_mean=UpperCamelCase_							)




		def 					lowerCAmelCase__       (	self					,     UpperCamelCase_					,     UpperCamelCase_					,     UpperCamelCase_ = None					,     UpperCamelCase_ = True					,     ):

							'''simple docstring'''


							if self.timesteps is None:
												raise ValueError(
												    '''`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler'''							)

							# For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
							# sample noise for correction
							UpperCamelCase__     :Any							      =				randn_tensor(sample.shape					,     layout=sample.layout					,     generator=UpperCamelCase_							).to(sample.device							)

							# compute step size from the model_output, the noise, and the snr
							UpperCamelCase__     :List[Any]							      =				torch.norm(model_output.reshape(model_output.shape[0]					,     -1							)					,     dim=-1							).mean()
							UpperCamelCase__     :Optional[Any]							      =				torch.norm(noise.reshape(noise.shape[0]					,     -1							)					,     dim=-1							).mean()
							UpperCamelCase__     :int							      =				(self.config.snr * noise_norm / grad_norm) ** 2 * 2
							UpperCamelCase__     :Dict							      =				step_size * torch.ones(sample.shape[0]							).to(sample.device							)
							# self.repeat_scalar(step_size, sample.shape[0])

							# compute corrected sample: model_output term and noise term
							UpperCamelCase__     :Union[str, Any]							      =				step_size.flatten()
							while len(step_size.shape							) < len(sample.shape							):
												UpperCamelCase__     :int							      =				step_size.unsqueeze(-1							)
							UpperCamelCase__     :List[str]							      =				sample + step_size * model_output
							UpperCamelCase__     :Optional[int]							      =				prev_sample_mean + ((step_size * 2) ** 0.5) * noise

							if not return_dict:
												return (prev_sample,)

							return SchedulerOutput(prev_sample=UpperCamelCase_							)




		def 					lowerCAmelCase__       (	self					,     UpperCamelCase_					,     UpperCamelCase_					,     UpperCamelCase_					,     ):

							'''simple docstring'''


							UpperCamelCase__     :List[Any]							      =				timesteps.to(original_samples.device							)
							UpperCamelCase__     :Union[str, Any]							      =				self.discrete_sigmas.to(original_samples.device							)[timesteps]
							UpperCamelCase__     :str							      =				(
							    noise * sigmas[:, None, None, None]
							    if noise is not None
							    else torch.randn_like(UpperCamelCase_							) * sigmas[:, None, None, None]
							)
							UpperCamelCase__     :Any							      =				noise + original_samples
							return noisy_samples




		def __len__(	self							):

							'''simple docstring'''


							return self.config.num_train_timesteps



'''simple docstring'''
import sys

__snake_case							   =  (
    '''73167176531330624919225119674426574742355349194934'''
    '''96983520312774506326239578318016984801869478851843'''
    '''85861560789112949495459501737958331952853208805511'''
    '''12540698747158523863050715693290963295227443043557'''
    '''66896648950445244523161731856403098711121722383113'''
    '''62229893423380308135336276614282806444486645238749'''
    '''30358907296290491560440772390713810515859307960866'''
    '''70172427121883998797908792274921901699720888093776'''
    '''65727333001053367881220235421809751254540594752243'''
    '''52584907711670556013604839586446706324415722155397'''
    '''53697817977846174064955149290862569321978468622482'''
    '''83972241375657056057490261407972968652414535100474'''
    '''82166370484403199890008895243450658541227588666881'''
    '''16427171479924442928230863465674813919123162824586'''
    '''17866458359124566529476545682848912883142607690042'''
    '''24219022671055626321111109370544217506941658960408'''
    '''07198403850962455444362981230987879927244284909188'''
    '''84580156166097919133875499200524063689912560717606'''
    '''05886116467109405077541002256983155200055935729725'''
    '''71636269561882670428252483600823257530420752963450'''
)


def     a   (    __a     )						->			int:



					'''simple docstring'''






					UpperCamelCase__     :Tuple							      =				1
					for digit in s:
										product *= int(__a     )
					return product


def     a   (    __a = N     )						->			int:



					'''simple docstring'''






					UpperCamelCase__     :Tuple							      =				-sys.maxsize - 1
					UpperCamelCase__     :Dict							      =				n[:13]
					UpperCamelCase__     :Dict							      =				13
					while cur_index < len(__a     ) - 13:
										if int(n[cur_index]     ) >= int(substr[0]     ):
															UpperCamelCase__     :Dict							      =				substr[1:] + n[cur_index]
															cur_index += 1
										else:
															UpperCamelCase__     :List[str]							      =				max(__a				,      str_eval(__a     )     )
															UpperCamelCase__     :Union[str, Any]							      =				n[cur_index : cur_index + 13]
															cur_index += 13
					return largest_product


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