





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

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin





@dataclass
class 	lowerCAmelCase__(       __lowercase			):






       '''simple docstring'''


       __snake_case       	=			42
       __snake_case       	=			42






def 			lowerCamelCase__	(__lowerCamelCase,				__lowerCamelCase=0.999,				__lowerCamelCase="cosine",				):
     if alpha_transform_type == "cosine":

          def alpha_bar_fn(__lowerCamelCase		):
               return math.cos((t + 0.008) / 1.008 * math.pi / 2		) ** 2

     elif alpha_transform_type == "exp":

          def alpha_bar_fn(__lowerCamelCase		):
               return math.exp(t * -12.0		)

     else:
          raise ValueError(f"""Unsupported alpha_tranform_type: {alpha_transform_type}"""		)

     _SCREAMING_SNAKE_CASE				:		Dict  			=							[]
     for i in range(__lowerCamelCase		):
          _SCREAMING_SNAKE_CASE				:		Tuple  			=							i / num_diffusion_timesteps
          _SCREAMING_SNAKE_CASE				:		List[str]  			=							(i + 1) / num_diffusion_timesteps
          betas.append(min(1 - alpha_bar_fn(__lowerCamelCase		) / alpha_bar_fn(__lowerCamelCase		),				__lowerCamelCase		)		)
     return torch.tensor(__lowerCamelCase,				dtype=torch.floataa		)





class 	lowerCAmelCase__(       __lowercase     ,   __lowercase			):






       '''simple docstring'''


       __snake_case       	=			1




       @register_to_config
       def __init__(					self			,  __lowerCamelCase = 1_0_0_0			,  __lowerCamelCase = 0.0001			,  __lowerCamelCase = 0.02			,  __lowerCamelCase = "linear"			,  __lowerCamelCase = 0.0			,  __lowerCamelCase = None			,  __lowerCamelCase = True			,  )	->   List[str]:
            if trained_betas is not None:
                 _SCREAMING_SNAKE_CASE				:		List[str]  			=							torch.from_numpy(__lowerCamelCase							)
            elif beta_schedule == "linear":
                 _SCREAMING_SNAKE_CASE				:		Any  			=							torch.linspace(__lowerCamelCase			,  __lowerCamelCase			,  __lowerCamelCase			,  dtype=torch.floataa							)
            elif beta_schedule == "scaled_linear":
                 # this schedule is very specific to the latent diffusion model.
                 _SCREAMING_SNAKE_CASE				:		List[Any]  			=							(
                     torch.linspace(beta_start**0.5			,  beta_end**0.5			,  __lowerCamelCase			,  dtype=torch.floataa							) ** 2
                 )
            elif beta_schedule == "squaredcos_cap_v2":
                 # Glide cosine schedule
                 _SCREAMING_SNAKE_CASE				:		str  			=							betas_for_alpha_bar(__lowerCamelCase							)
            elif beta_schedule == "sigmoid":
                 # GeoDiff sigmoid schedule
                 _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							torch.linspace(-6			,  6			,  __lowerCamelCase							)
                 _SCREAMING_SNAKE_CASE				:		str  			=							torch.sigmoid(__lowerCamelCase							) * (beta_end - beta_start) + beta_start
            else:
                 raise NotImplementedError(F"""{beta_schedule} does is not implemented for {self.__class__}"""							)

            _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							1.0 - self.betas
            _SCREAMING_SNAKE_CASE				:		Optional[int]  			=							torch.cumprod(self.alphas			,  dim=0							)
            _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							torch.tensor(1.0							)

            _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							torch.tensor(1.0							)

            # standard deviation of the initial noise distribution
            _SCREAMING_SNAKE_CASE				:		List[str]  			=							1.0

            # setable values
            _SCREAMING_SNAKE_CASE				:		List[str]  			=							None
            _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							torch.from_numpy(np.arange(0			,  __lowerCamelCase							)[::-1].copy()							)

            _SCREAMING_SNAKE_CASE				:		Any  			=							eta




       def 			UpperCamelCase_	(					self			,  __lowerCamelCase			,  __lowerCamelCase = None							)	->   torch.FloatTensor:
            return sample




       def 			UpperCamelCase_	(					self			,  __lowerCamelCase			,  __lowerCamelCase = 1_0			,  __lowerCamelCase = 1_0			,  __lowerCamelCase = None			,  )	->   int:
            _SCREAMING_SNAKE_CASE				:		Any  			=							min(self.config.num_train_timesteps			,  __lowerCamelCase							)
            _SCREAMING_SNAKE_CASE				:		List[str]  			=							num_inference_steps

            _SCREAMING_SNAKE_CASE				:		List[str]  			=							[]

            _SCREAMING_SNAKE_CASE				:		Optional[int]  			=							{}
            for j in range(0			,  num_inference_steps - jump_length			,  __lowerCamelCase							):
                 _SCREAMING_SNAKE_CASE				:		Any  			=							jump_n_sample - 1

            _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							num_inference_steps
            while t >= 1:
                 _SCREAMING_SNAKE_CASE				:		List[Any]  			=							t - 1
                 timesteps.append(__lowerCamelCase							)

                 if jumps.get(__lowerCamelCase			,  0							) > 0:
                      _SCREAMING_SNAKE_CASE				:		int  			=							jumps[t] - 1
                      for _ in range(__lowerCamelCase							):
                           _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							t + 1
                           timesteps.append(__lowerCamelCase							)

            _SCREAMING_SNAKE_CASE				:		List[str]  			=							np.array(__lowerCamelCase							) * (self.config.num_train_timesteps // self.num_inference_steps)
            _SCREAMING_SNAKE_CASE				:		List[Any]  			=							torch.from_numpy(__lowerCamelCase							).to(__lowerCamelCase							)




       def 			UpperCamelCase_	(					self			,  __lowerCamelCase							)	->   List[str]:
            _SCREAMING_SNAKE_CASE				:		Optional[int]  			=							t - self.config.num_train_timesteps // self.num_inference_steps

            _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							self.alphas_cumprod[t]
            _SCREAMING_SNAKE_CASE				:		int  			=							self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
            _SCREAMING_SNAKE_CASE				:		List[Any]  			=							1 - alpha_prod_t
            _SCREAMING_SNAKE_CASE				:		Tuple  			=							1 - alpha_prod_t_prev

            # For t > 0, compute predicted variance βt (see formula (6) and (7) from
            # https://arxiv.org/pdf/2006.11239.pdf) and sample from it to get
            # previous sample x_{t-1} ~ N(pred_prev_sample, variance) == add
            # variance to pred_sample
            # Is equivalent to formula (16) in https://arxiv.org/pdf/2010.02502.pdf
            # without eta.
            # variance = (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * self.betas[t]
            _SCREAMING_SNAKE_CASE				:		Tuple  			=							(beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

            return variance




       def 			UpperCamelCase_	(					self			,  __lowerCamelCase			,  __lowerCamelCase			,  __lowerCamelCase			,  __lowerCamelCase			,  __lowerCamelCase			,  __lowerCamelCase = None			,  __lowerCamelCase = True			,  )	->   Union[RePaintSchedulerOutput, Tuple]:
            _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							timestep
            _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							timestep - self.config.num_train_timesteps // self.num_inference_steps

            # 1. compute alphas, betas
            _SCREAMING_SNAKE_CASE				:		Any  			=							self.alphas_cumprod[t]
            _SCREAMING_SNAKE_CASE				:		Optional[int]  			=							self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
            _SCREAMING_SNAKE_CASE				:		str  			=							1 - alpha_prod_t

            # 2. compute predicted original sample from predicted noise also called
            # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
            _SCREAMING_SNAKE_CASE				:		Any  			=							(sample - beta_prod_t**0.5 * model_output) / alpha_prod_t**0.5

            # 3. Clip "predicted x_0"
            if self.config.clip_sample:
                 _SCREAMING_SNAKE_CASE				:		Tuple  			=							torch.clamp(__lowerCamelCase			,  -1			,  1							)

            # We choose to follow RePaint Algorithm 1 to get x_{t-1}, however we
            # substitute formula (7) in the algorithm coming from DDPM paper
            # (formula (4) Algorithm 2 - Sampling) with formula (12) from DDIM paper.
            # DDIM schedule gives the same results as DDPM with eta = 1.0
            # Noise is being reused in 7. and 8., but no impact on quality has
            # been observed.

            # 5. Add noise
            _SCREAMING_SNAKE_CASE				:		Any  			=							model_output.device
            _SCREAMING_SNAKE_CASE				:		List[Any]  			=							randn_tensor(model_output.shape			,  generator=__lowerCamelCase			,  device=__lowerCamelCase			,  dtype=model_output.dtype							)
            _SCREAMING_SNAKE_CASE				:		str  			=							self.eta * self._get_variance(__lowerCamelCase							) ** 0.5

            _SCREAMING_SNAKE_CASE				:		Dict  			=							0
            if t > 0 and self.eta > 0:
                 _SCREAMING_SNAKE_CASE				:		Dict  			=							std_dev_t * noise

            # 6. compute "direction pointing to x_t" of formula (12)
            # from https://arxiv.org/pdf/2010.02502.pdf
            _SCREAMING_SNAKE_CASE				:		List[str]  			=							(1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * model_output

            # 7. compute x_{t-1} of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
            _SCREAMING_SNAKE_CASE				:		Tuple  			=							alpha_prod_t_prev**0.5 * pred_original_sample + pred_sample_direction + variance

            # 8. Algorithm 1 Line 5 https://arxiv.org/pdf/2201.09865.pdf
            _SCREAMING_SNAKE_CASE				:		List[Any]  			=							(alpha_prod_t_prev**0.5) * original_image + ((1 - alpha_prod_t_prev) ** 0.5) * noise

            # 9. Algorithm 1 Line 8 https://arxiv.org/pdf/2201.09865.pdf
            _SCREAMING_SNAKE_CASE				:		List[str]  			=							mask * prev_known_part + (1.0 - mask) * prev_unknown_part

            if not return_dict:
                 return (
                     pred_prev_sample,
                     pred_original_sample,
                 )

            return RePaintSchedulerOutput(prev_sample=__lowerCamelCase			,  pred_original_sample=__lowerCamelCase							)




       def 			UpperCamelCase_	(					self			,  __lowerCamelCase			,  __lowerCamelCase			,  __lowerCamelCase=None							)	->   Union[str, Any]:
            _SCREAMING_SNAKE_CASE				:		str  			=							self.config.num_train_timesteps // self.num_inference_steps

            for i in range(__lowerCamelCase							):
                 _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							self.betas[timestep + i]
                 if sample.device.type == "mps":
                      # randn does not work reproducibly on mps
                      _SCREAMING_SNAKE_CASE				:		List[Any]  			=							randn_tensor(sample.shape			,  dtype=sample.dtype			,  generator=__lowerCamelCase							)
                      _SCREAMING_SNAKE_CASE				:		Any  			=							noise.to(sample.device							)
                 else:
                      _SCREAMING_SNAKE_CASE				:		Any  			=							randn_tensor(sample.shape			,  generator=__lowerCamelCase			,  device=sample.device			,  dtype=sample.dtype							)

                 # 10. Algorithm 1 Line 10 https://arxiv.org/pdf/2201.09865.pdf
                 _SCREAMING_SNAKE_CASE				:		List[Any]  			=							(1 - beta) ** 0.5 * sample + beta**0.5 * noise

            return sample




       def 			UpperCamelCase_	(					self			,  __lowerCamelCase			,  __lowerCamelCase			,  __lowerCamelCase			,  )	->   torch.FloatTensor:
            raise NotImplementedError("Use `DDPMScheduler.add_noise()` to train for sampling with RePaint."							)







       def __len__(					self							)	->   Tuple:
            return self.config.num_train_timesteps






from itertools import permutations






def 			lowerCamelCase__	():
     _SCREAMING_SNAKE_CASE				:		Dict  			=							list(map("".join,				permutations("0123456789"		)		)		)
     return result[999999]


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