



# 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 					_snake_case      (       SCREAMING_SNAKE_CASE__):
				UpperCamelCase__					:       Union[str, Any]  		=4_2
				UpperCamelCase__					:       Dict  		=4_2
class 					_snake_case      (       SCREAMING_SNAKE_CASE__     ,						SCREAMING_SNAKE_CASE__):
				UpperCamelCase__					:       List[str]  		=1




				@register_to_config
				def __init__(    self       :    Union[str, Any],       __lowercase       :    int = 2000,       __lowercase       :    float = 0.15,       __lowercase       :    float = 0.01,       __lowercase       :    float = 1348.0,       __lowercase       :    float = 1e-5,       __lowercase       :    int = 1,       ):
							lowercase__       	=					sigma_max

							# setable values
							lowercase__       	=					None

							self.set_sigmas(snake_case__,       snake_case__,       snake_case__,       snake_case__    )




				def 				A__   (    self       :    Optional[int],       __lowercase       :    torch.FloatTensor,       __lowercase       :    Optional[int] = None    ):
							return sample




				def 				A__   (    self       :    Dict,       __lowercase       :    int,       __lowercase       :    float = None,       __lowercase       :    Union[str, torch.device] = None    ):
							lowercase__       	=					sampling_eps if sampling_eps is not None else self.config.sampling_eps

							lowercase__       	=					torch.linspace(1,       snake_case__,       snake_case__,       device=snake_case__    )




				def 				A__   (    self       :    Union[str, Any],       __lowercase       :    int,       __lowercase       :    float = None,       __lowercase       :    float = None,       __lowercase       :    float = None    ):
							lowercase__       	=					sigma_min if sigma_min is not None else self.config.sigma_min
							lowercase__       	=					sigma_max if sigma_max is not None else self.config.sigma_max
							lowercase__       	=					sampling_eps if sampling_eps is not None else self.config.sampling_eps
							if self.timesteps is None:
										self.set_timesteps(snake_case__,       snake_case__    )

							lowercase__       	=					sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
							lowercase__       	=					torch.exp(torch.linspace(math.log(snake_case__    ),       math.log(snake_case__    ),       snake_case__    )    )
							lowercase__       	=					torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps]    )




				def 				A__   (    self       :    Any,       __lowercase       :    int,       __lowercase       :    List[str]    ):
							return torch.where(
							    timesteps == 0,       torch.zeros_like(t.to(timesteps.device    )    ),       self.discrete_sigmas[timesteps - 1].to(timesteps.device    ),       )




				def 				A__   (    self       :    Union[str, Any],       __lowercase       :    torch.FloatTensor,       __lowercase       :    int,       __lowercase       :    torch.FloatTensor,       __lowercase       :    Optional[torch.Generator] = None,       __lowercase       :    bool = True,       ):

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

							lowercase__       	=					timestep * torch.ones(
							    sample.shape[0],       device=sample.device    )  # torch.repeat_interleave(timestep, sample.shape[0])
							lowercase__       	=					(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
							lowercase__       	=					timesteps.to(self.discrete_sigmas.device    )

							lowercase__       	=					self.discrete_sigmas[timesteps].to(sample.device    )
							lowercase__       	=					self.get_adjacent_sigma(snake_case__,       snake_case__    ).to(sample.device    )
							lowercase__       	=					torch.zeros_like(snake_case__    )
							lowercase__       	=					(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
							lowercase__       	=					diffusion.flatten()
							while len(diffusion.shape    ) < len(sample.shape    ):
										lowercase__       	=					diffusion.unsqueeze(-1    )
							lowercase__       	=					drift - diffusion**2 * model_output

							#  equation 6: sample noise for the diffusion term of
							lowercase__       	=					randn_tensor(
							    sample.shape,       layout=sample.layout,       generator=snake_case__,       device=sample.device,       dtype=sample.dtype    )
							lowercase__       	=					sample - drift  # subtract because `dt` is a small negative timestep
							# TODO is the variable diffusion the correct scaling term for the noise?
							lowercase__       	=					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=snake_case__,       prev_sample_mean=snake_case__    )




				def 				A__   (    self       :    int,       __lowercase       :    torch.FloatTensor,       __lowercase       :    torch.FloatTensor,       __lowercase       :    Optional[torch.Generator] = None,       __lowercase       :    bool = True,       ):

							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
							lowercase__       	=					randn_tensor(sample.shape,       layout=sample.layout,       generator=snake_case__    ).to(sample.device    )

							# compute step size from the model_output, the noise, and the snr
							lowercase__       	=					torch.norm(model_output.reshape(model_output.shape[0],       -1    ),       dim=-1    ).mean()
							lowercase__       	=					torch.norm(noise.reshape(noise.shape[0],       -1    ),       dim=-1    ).mean()
							lowercase__       	=					(self.config.snr * noise_norm / grad_norm) ** 2 * 2
							lowercase__       	=					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
							lowercase__       	=					step_size.flatten()
							while len(step_size.shape    ) < len(sample.shape    ):
										lowercase__       	=					step_size.unsqueeze(-1    )
							lowercase__       	=					sample + step_size * model_output
							lowercase__       	=					prev_sample_mean + ((step_size * 2) ** 0.5) * noise

							if not return_dict:
										return (prev_sample,)

							return SchedulerOutput(prev_sample=snake_case__    )




				def 				A__   (    self       :    Tuple,       __lowercase       :    torch.FloatTensor,       __lowercase       :    torch.FloatTensor,       __lowercase       :    torch.FloatTensor,       ):
							lowercase__       	=					timesteps.to(original_samples.device    )
							lowercase__       	=					self.discrete_sigmas.to(original_samples.device    )[timesteps]
							lowercase__       	=					(
							    noise * sigmas[:, None, None, None]
							    if noise is not None
							    else torch.randn_like(snake_case__    ) * sigmas[:, None, None, None]
							)
							lowercase__       	=					noise + original_samples
							return noisy_samples




				def __len__(    self       :    Any    ):
							return self.config.num_train_timesteps










SCREAMING_SNAKE_CASE:     dict[tuple[int, int, int], int]									= {}


def 					_a							(					lowerCAmelCase    ,						lowerCAmelCase    ,						lowerCAmelCase )->	int:

		# if we are absent twice, or late 3 consecutive days,
		# no further prize strings are possible
		if late == 3 or absent == 2:
				return 0

		# if we have no days left, and have not failed any other rules,
		# we have a prize string
		if days == 0:
				return 1

		# No easy solution, so now we need to do the recursive calculation

		# First, check if the combination is already in the cache, and
		# if yes, return the stored value from there since we already
		# know the number of possible prize strings from this point on
		SCREAMING_SNAKE_CASE_					      =							(days, absent, late)
		if key in cache:
				return cache[key]

		# now we calculate the three possible ways that can unfold from
		# this point on, depending on our attendance today

		# 1) if we are late (but not absent), the "absent" counter stays as
		# it is, but the "late" counter increases by one
		SCREAMING_SNAKE_CASE_					      =							_calculate(days - 1    ,						lowerCAmelCase    ,						late + 1 )

		# 2) if we are absent, the "absent" counter increases by 1, and the
		# "late" counter resets to 0
		SCREAMING_SNAKE_CASE_					      =							_calculate(days - 1    ,						absent + 1    ,						0 )

		# 3) if we are on time, this resets the "late" counter and keeps the
		# absent counter
		SCREAMING_SNAKE_CASE_					      =							_calculate(days - 1    ,						lowerCAmelCase    ,						0 )

		SCREAMING_SNAKE_CASE_					      =							state_late + state_absent + state_ontime

		SCREAMING_SNAKE_CASE_					      =							prizestrings
		return prizestrings


def 					_a							(					lowerCAmelCase = 30 )->	int:
		return _calculate(lowerCAmelCase    ,						absent=0    ,						late=0 )


if __name__ == "__main__":
						print(solution())