"""simple docstring"""






def      UpperCAmelCase__			(							lowerCAmelCase__	:int = 1_0_0_0						)					->       int:
      '''simple docstring'''


      return sum(e for e in range(3   ,						lowerCAmelCase__						) if e % 3 == 0 or e % 5 == 0						)


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




"""simple docstring"""






from typing import Optional, Tuple, Union

import torch
from einops import rearrange, reduce

from diffusers import DDIMScheduler, DDPMScheduler, DiffusionPipeline, ImagePipelineOutput, UNetaDConditionModel
from diffusers.schedulers.scheduling_ddim import DDIMSchedulerOutput
from diffusers.schedulers.scheduling_ddpm import DDPMSchedulerOutput


__lowerCAmelCase       :			Tuple   	=8


def      UpperCAmelCase__			(							lowerCAmelCase__	:str   ,						lowerCAmelCase__	:int=BITS						)					->       Optional[Any]:
      '''simple docstring'''


      lowercase								=      x.device

      lowercase								=      (x * 2_5_5).int().clamp(0   ,						2_5_5						)

      lowercase								=      2 ** torch.arange(bits - 1   ,						-1   ,						-1   ,						device=lowerCAmelCase__						)
      lowercase								=      rearrange(lowerCAmelCase__   ,						"""d -> d 1 1"""						)
      lowercase								=      rearrange(lowerCAmelCase__   ,						"""b c h w -> b c 1 h w"""						)

      lowercase								=      ((x & mask) != 0).float()
      lowercase								=      rearrange(lowerCAmelCase__   ,						"""b c d h w -> b (c d) h w"""						)
      lowercase								=      bits * 2 - 1
      return bits


def      UpperCAmelCase__			(							lowerCAmelCase__	:Dict   ,						lowerCAmelCase__	:int=BITS						)					->       List[Any]:
      '''simple docstring'''


      lowercase								=      x.device

      lowercase								=      (x > 0).int()
      lowercase								=      2 ** torch.arange(bits - 1   ,						-1   ,						-1   ,						device=lowerCAmelCase__   ,						dtype=torch.intaa						)

      lowercase								=      rearrange(lowerCAmelCase__   ,						"""d -> d 1 1"""						)
      lowercase								=      rearrange(lowerCAmelCase__   ,						"""b (c d) h w -> b c d h w"""   ,						d=8						)
      lowercase								=      reduce(x * mask   ,						"""b c d h w -> b c h w"""   ,						"""sum"""						)
      return (dec / 2_5_5).clamp(0.0   ,						1.0						)


def      UpperCAmelCase__			(							self	:Union[str, Any]   ,						lowerCAmelCase__	:torch.FloatTensor   ,						lowerCAmelCase__	:int   ,						lowerCAmelCase__	:torch.FloatTensor   ,						lowerCAmelCase__	:float = 0.0   ,						lowerCAmelCase__	:bool = True   ,						lowerCAmelCase__	:Optional[Any]=None   ,						lowerCAmelCase__	:bool = True   ,						)					->       Union[DDIMSchedulerOutput, Tuple]:
      '''simple docstring'''


      if self.num_inference_steps is None:
            raise ValueError(
                """Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"""						)

      # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
      # Ideally, read DDIM paper in-detail understanding

      # Notation (<variable name> -> <name in paper>
      # - pred_noise_t -> e_theta(x_t, t)
      # - pred_original_sample -> f_theta(x_t, t) or x_0
      # - std_dev_t -> sigma_t
      # - eta -> η
      # - pred_sample_direction -> "direction pointing to x_t"
      # - pred_prev_sample -> "x_t-1"

      # 1. get previous step value (=t-1)
      lowercase								=      timestep - self.config.num_train_timesteps // self.num_inference_steps

      # 2. compute alphas, betas
      lowercase								=      self.alphas_cumprod[timestep]
      lowercase								=      self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod

      lowercase								=      1 - alpha_prod_t

      # 3. compute predicted original sample from predicted noise also called
      # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
      lowercase								=      (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5

      # 4. Clip "predicted x_0"
      lowercase								=      self.bit_scale
      if self.config.clip_sample:
            lowercase								=      torch.clamp(lowerCAmelCase__   ,						-scale   ,						lowerCAmelCase__						)

      # 5. compute variance: "sigma_t(η)" -> see formula (16)
      # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
      lowercase								=      self._get_variance(lowerCAmelCase__   ,						lowerCAmelCase__						)
      lowercase								=      eta * variance ** 0.5

      if use_clipped_model_output:
            # the model_output is always re-derived from the clipped x_0 in Glide
            lowercase								=      (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5

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

      # 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
      lowercase								=      alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

      if eta > 0:
            # randn_like does not support generator https://github.com/pytorch/pytorch/issues/27072
            lowercase								=      model_output.device if torch.is_tensor(lowerCAmelCase__						) else """cpu"""
            lowercase								=      torch.randn(model_output.shape   ,						dtype=model_output.dtype   ,						generator=lowerCAmelCase__						).to(lowerCAmelCase__						)
            lowercase								=      self._get_variance(lowerCAmelCase__   ,						lowerCAmelCase__						) ** 0.5 * eta * noise

            lowercase								=      prev_sample + variance

      if not return_dict:
            return (prev_sample,)

      return DDIMSchedulerOutput(prev_sample=lowerCAmelCase__   ,						pred_original_sample=lowerCAmelCase__						)


def      UpperCAmelCase__			(							self	:Any   ,						lowerCAmelCase__	:torch.FloatTensor   ,						lowerCAmelCase__	:int   ,						lowerCAmelCase__	:torch.FloatTensor   ,						lowerCAmelCase__	:List[str]="epsilon"   ,						lowerCAmelCase__	:Optional[int]=None   ,						lowerCAmelCase__	:bool = True   ,						)					->       Union[DDPMSchedulerOutput, Tuple]:
      '''simple docstring'''


      lowercase								=      timestep

      if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type in ["learned", "learned_range"]:
            lowercase				,				lowercase								=      torch.split(lowerCAmelCase__   ,						sample.shape[1]   ,						dim=1						)
      else:
            lowercase								=      None

      # 1. compute alphas, betas
      lowercase								=      self.alphas_cumprod[t]
      lowercase								=      self.alphas_cumprod[t - 1] if t > 0 else self.one
      lowercase								=      1 - alpha_prod_t
      lowercase								=      1 - alpha_prod_t_prev

      # 2. compute predicted original sample from predicted noise also called
      # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
      if prediction_type == "epsilon":
            lowercase								=      (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
      elif prediction_type == "sample":
            lowercase								=      model_output
      else:
            raise ValueError(f'Unsupported prediction_type {prediction_type}.'						)

      # 3. Clip "predicted x_0"
      lowercase								=      self.bit_scale
      if self.config.clip_sample:
            lowercase								=      torch.clamp(lowerCAmelCase__   ,						-scale   ,						lowerCAmelCase__						)

      # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
      # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
      lowercase								=      (alpha_prod_t_prev ** 0.5 * self.betas[t]) / beta_prod_t
      lowercase								=      self.alphas[t] ** 0.5 * beta_prod_t_prev / beta_prod_t

      # 5. Compute predicted previous sample µ_t
      # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
      lowercase								=      pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

      # 6. Add noise
      lowercase								=      0
      if t > 0:
            lowercase								=      torch.randn(
                model_output.size()   ,						dtype=model_output.dtype   ,						layout=model_output.layout   ,						generator=lowerCAmelCase__						).to(model_output.device						)
            lowercase								=      (self._get_variance(lowerCAmelCase__   ,						predicted_variance=lowerCAmelCase__						) ** 0.5) * noise

      lowercase								=      pred_prev_sample + variance

      if not return_dict:
            return (pred_prev_sample,)

      return DDPMSchedulerOutput(prev_sample=lowerCAmelCase__   ,						pred_original_sample=lowerCAmelCase__						)






class 					_A		(			lowerCAmelCase      ):

      def __init__(		self						,			__lowerCAmelCase						,			__lowerCAmelCase						,			__lowerCAmelCase = 1.0						,			):







            """simple docstring"""



            super().__init__()
            lowercase								=      bit_scale
            lowercase								=      (
                ddim_bit_scheduler_step if isinstance(__lowerCAmelCase						,			__lowerCAmelCase		) else ddpm_bit_scheduler_step
            )

            self.register_modules(unet=__lowerCAmelCase						,			scheduler=__lowerCAmelCase		)







      @torch.no_grad()
      def __call__(		self						,			__lowerCAmelCase = 256						,			__lowerCAmelCase = 256						,			__lowerCAmelCase = 50						,			__lowerCAmelCase = None						,			__lowerCAmelCase = 1						,			__lowerCAmelCase = "pil"						,			__lowerCAmelCase = True						,			**__lowerCAmelCase						,			):







            """simple docstring"""



            lowercase								=      torch.randn(
                (batch_size, self.unet.config.in_channels, height, width)						,			generator=__lowerCAmelCase						,			)
            lowercase								=      decimal_to_bits(__lowerCAmelCase		) * self.bit_scale
            lowercase								=      latents.to(self.device		)

            self.scheduler.set_timesteps(__lowerCAmelCase		)

            for t in self.progress_bar(self.scheduler.timesteps		):
                  # predict the noise residual
                  lowercase								=      self.unet(__lowerCAmelCase						,			__lowerCAmelCase		).sample

                  # compute the previous noisy sample x_t -> x_t-1
                  lowercase								=      self.scheduler.step(__lowerCAmelCase						,			__lowerCAmelCase						,			__lowerCAmelCase		).prev_sample

            lowercase								=      bits_to_decimal(__lowerCAmelCase		)

            if output_type == "pil":
                  lowercase								=      self.numpy_to_pil(__lowerCAmelCase		)

            if not return_dict:
                  return (image,)

            return ImagePipelineOutput(images=__lowerCAmelCase		)



