"""simple docstring"""


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 					UpperCamelCase   (							lowerCAmelCase__  ):
       SCREAMING_SNAKE_CASE_						      = 42
       SCREAMING_SNAKE_CASE_						      = 42







def    UpperCAmelCase       (						UpperCAmelCase		,   UpperCAmelCase=0.999		,   UpperCAmelCase="cosine"		,   )							-> Dict:
     if alpha_transform_type == "cosine":

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

     elif alpha_transform_type == "exp":

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

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

     snake_case_   			=   []
     for i in range(UpperCAmelCase   ):
          snake_case_   			=   i / num_diffusion_timesteps
          snake_case_   			=   (i + 1) / num_diffusion_timesteps
          betas.append(min(1 - alpha_bar_fn(UpperCAmelCase   ) / alpha_bar_fn(UpperCAmelCase   )		,   UpperCAmelCase   )   )
     return torch.tensor(UpperCAmelCase		,   dtype=torch.floataa   )




class 					UpperCamelCase   (							lowerCAmelCase__       ,						lowerCAmelCase__  ):
       SCREAMING_SNAKE_CASE_						      = 1







       @register_to_config
       def __init__(					self,				lowerCAmelCase__ = 1000,				lowerCAmelCase__ = 0.0001,				lowerCAmelCase__ = 0.02,				lowerCAmelCase__ = "linear",				lowerCAmelCase__ = 0.0,				lowerCAmelCase__ = None,				lowerCAmelCase__ = True,				) -> Tuple:
            if trained_betas is not None:
                 snake_case_   			=   torch.from_numpy(lowerCAmelCase__)
            elif beta_schedule == "linear":
                 snake_case_   			=   torch.linspace(lowerCAmelCase__,				lowerCAmelCase__,				lowerCAmelCase__,				dtype=torch.floataa)
            elif beta_schedule == "scaled_linear":
                 # this schedule is very specific to the latent diffusion model.
                 snake_case_   			=   (
                     torch.linspace(beta_start**0.5,				beta_end**0.5,				lowerCAmelCase__,				dtype=torch.floataa) ** 2
                 )
            elif beta_schedule == "squaredcos_cap_v2":
                 # Glide cosine schedule
                 snake_case_   			=   betas_for_alpha_bar(lowerCAmelCase__)
            elif beta_schedule == "sigmoid":
                 # GeoDiff sigmoid schedule
                 snake_case_   			=   torch.linspace(-6,				6,				lowerCAmelCase__)
                 snake_case_   			=   torch.sigmoid(lowerCAmelCase__) * (beta_end - beta_start) + beta_start
            else:
                 raise NotImplementedError(f'{beta_schedule} does is not implemented for {self.__class__}')

            snake_case_   			=   1.0 - self.betas
            snake_case_   			=   torch.cumprod(self.alphas,				dim=0)
            snake_case_   			=   torch.tensor(1.0)

            snake_case_   			=   torch.tensor(1.0)

            # standard deviation of the initial noise distribution
            snake_case_   			=   1.0

            # setable values
            snake_case_   			=   None
            snake_case_   			=   torch.from_numpy(np.arange(0,				lowerCAmelCase__)[::-1].copy())

            snake_case_   			=   eta







       def 						a_		(					self,				lowerCAmelCase__,				lowerCAmelCase__ = None) -> torch.FloatTensor:
            return sample







       def 						a_		(					self,				lowerCAmelCase__,				lowerCAmelCase__ = 10,				lowerCAmelCase__ = 10,				lowerCAmelCase__ = None,				) -> Union[str, Any]:
            snake_case_   			=   min(self.config.num_train_timesteps,				lowerCAmelCase__)
            snake_case_   			=   num_inference_steps

            snake_case_   			=   []

            snake_case_   			=   {}
            for j in range(0,				num_inference_steps - jump_length,				lowerCAmelCase__):
                 snake_case_   			=   jump_n_sample - 1

            snake_case_   			=   num_inference_steps
            while t >= 1:
                 snake_case_   			=   t - 1
                 timesteps.append(lowerCAmelCase__)

                 if jumps.get(lowerCAmelCase__,				0) > 0:
                      snake_case_   			=   jumps[t] - 1
                      for _ in range(lowerCAmelCase__):
                           snake_case_   			=   t + 1
                           timesteps.append(lowerCAmelCase__)

            snake_case_   			=   np.array(lowerCAmelCase__) * (self.config.num_train_timesteps // self.num_inference_steps)
            snake_case_   			=   torch.from_numpy(lowerCAmelCase__).to(lowerCAmelCase__)







       def 						a_		(					self,				lowerCAmelCase__) -> Tuple:
            snake_case_   			=   t - self.config.num_train_timesteps // self.num_inference_steps

            snake_case_   			=   self.alphas_cumprod[t]
            snake_case_   			=   self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
            snake_case_   			=   1 - alpha_prod_t
            snake_case_   			=   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]
            snake_case_   			=   (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

            return variance







       def 						a_		(					self,				lowerCAmelCase__,				lowerCAmelCase__,				lowerCAmelCase__,				lowerCAmelCase__,				lowerCAmelCase__,				lowerCAmelCase__ = None,				lowerCAmelCase__ = True,				) -> Union[RePaintSchedulerOutput, Tuple]:
            snake_case_   			=   timestep
            snake_case_   			=   timestep - self.config.num_train_timesteps // self.num_inference_steps

            # 1. compute alphas, betas
            snake_case_   			=   self.alphas_cumprod[t]
            snake_case_   			=   self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
            snake_case_   			=   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
            snake_case_   			=   (sample - beta_prod_t**0.5 * model_output) / alpha_prod_t**0.5

            # 3. Clip "predicted x_0"
            if self.config.clip_sample:
                 snake_case_   			=   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
            snake_case_   			=   model_output.device
            snake_case_   			=   randn_tensor(model_output.shape,				generator=lowerCAmelCase__,				device=lowerCAmelCase__,				dtype=model_output.dtype)
            snake_case_   			=   self.eta * self._get_variance(lowerCAmelCase__) ** 0.5

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

            # 6. compute "direction pointing to x_t" of formula (12)
            # from https://arxiv.org/pdf/2010.02502.pdf
            snake_case_   			=   (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
            snake_case_   			=   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
            snake_case_   			=   (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
            snake_case_   			=   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 						a_		(					self,				lowerCAmelCase__,				lowerCAmelCase__,				lowerCAmelCase__=None) -> Tuple:
            snake_case_   			=   self.config.num_train_timesteps // self.num_inference_steps

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

                 # 10. Algorithm 1 Line 10 https://arxiv.org/pdf/2201.09865.pdf
                 snake_case_   			=   (1 - beta) ** 0.5 * sample + beta**0.5 * noise

            return sample







       def 						a_		(					self,				lowerCAmelCase__,				lowerCAmelCase__,				lowerCAmelCase__,				) -> torch.FloatTensor:
            raise NotImplementedError('Use `DDPMScheduler.add_noise()` to train for sampling with RePaint.')







       def __len__(					self) -> List[Any]:
            return self.config.num_train_timesteps


"""simple docstring"""


from math import factorial







def    UpperCAmelCase       (						UpperCAmelCase		,   UpperCAmelCase   )							-> List[str]:
     return factorial(UpperCAmelCase   ) / (factorial(UpperCAmelCase   ) * factorial(n - r   ))







def    UpperCAmelCase       (						)							-> Optional[Any]:
     snake_case_   			=   0

     for i in range(1		,   101   ):
          for j in range(1		,   i + 1   ):
               if combinations(UpperCAmelCase		,   UpperCAmelCase   ) > 1e6:
                    total += 1
     return total


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

