

'''simple docstring'''
from math import acos, sin
from typing import List, Tuple, Union

import numpy as np
import torch
from PIL import Image

from ...models import AutoencoderKL, UNetaDConditionModel
from ...schedulers import DDIMScheduler, DDPMScheduler
from ...utils import randn_tensor
from ..pipeline_utils import AudioPipelineOutput, BaseOutput, DiffusionPipeline, ImagePipelineOutput
from .mel import Mel


class        a__  (							a_  ):
   _SCREAMING_SNAKE_CASE   :					str     	=							['''vqvae''']


   def __init__(			self      ,    _UpperCamelCase      ,    _UpperCamelCase      ,    _UpperCamelCase      ,    _UpperCamelCase      ,    ):





      """simple docstring"""





      super().__init__()
      self.register_modules(unet=lowercase_      ,    scheduler=lowercase_      ,    mel=lowercase_      ,    vqvae=lowercase_  )


   def 						_lowerCamelCase       (			self  ):





      """simple docstring"""





      return 50 if isinstance(self.scheduler      ,    lowercase_  ) else 1000


   @torch.no_grad()
   def __call__(			self      ,    _UpperCamelCase = 1      ,    _UpperCamelCase = None      ,    _UpperCamelCase = None      ,    _UpperCamelCase = 0      ,    _UpperCamelCase = 0      ,    _UpperCamelCase = None      ,    _UpperCamelCase = None      ,    _UpperCamelCase = 0      ,    _UpperCamelCase = 0      ,    _UpperCamelCase = None      ,    _UpperCamelCase = 0      ,    _UpperCamelCase = None      ,    _UpperCamelCase = None      ,    _UpperCamelCase=True      ,    ):





      """simple docstring"""





      _lowercase      :				List[Any]      					=       steps or self.get_default_steps()
      self.scheduler.set_timesteps(lowercase_  )
      _lowercase      :				Optional[int]      					=       step_generator or generator
      # For backwards compatibility
      if type(self.unet.config.sample_size  ) == int:
         _lowercase      :				int      					=       (self.unet.config.sample_size, self.unet.config.sample_size)
      if noise is None:
         _lowercase      :				List[str]      					=       randn_tensor(
             (
                 batch_size,
                 self.unet.config.in_channels,
                 self.unet.config.sample_size[0],
                 self.unet.config.sample_size[1],
             )      ,    generator=lowercase_      ,    device=self.device      ,    )
      _lowercase      :				Tuple      					=       noise
      _lowercase      :				Tuple      					=       None

      if audio_file is not None or raw_audio is not None:
         self.mel.load_audio(lowercase_      ,    lowercase_  )
         _lowercase      :				List[str]      					=       self.mel.audio_slice_to_image(lowercase_  )
         _lowercase      :				List[str]      					=       np.frombuffer(input_image.tobytes()      ,    dtype="uint8"  ).reshape(
             (input_image.height, input_image.width)  )
         _lowercase      :				Union[str, Any]      					=       (input_image / 255) * 2 - 1
         _lowercase      :				Optional[int]      					=       torch.tensor(input_image[np.newaxis, :, :]      ,    dtype=torch.float  ).to(self.device  )

         if self.vqvae is not None:
            _lowercase      :				int      					=       self.vqvae.encode(torch.unsqueeze(lowercase_      ,    0  )  ).latent_dist.sample(
                generator=lowercase_  )[0]
            _lowercase      :				Any      					=       self.vqvae.config.scaling_factor * input_images

         if start_step > 0:
            _lowercase      :				Optional[Any]      					=       self.scheduler.add_noise(lowercase_      ,    lowercase_      ,    self.scheduler.timesteps[start_step - 1]  )

         _lowercase      :				List[Any]      					=       (
             self.unet.config.sample_size[1] * self.mel.get_sample_rate() / self.mel.x_res / self.mel.hop_length
         )
         _lowercase      :				List[str]      					=       int(mask_start_secs * pixels_per_second  )
         _lowercase      :				Optional[int]      					=       int(mask_end_secs * pixels_per_second  )
         _lowercase      :				Dict      					=       self.scheduler.add_noise(lowercase_      ,    lowercase_      ,    torch.tensor(self.scheduler.timesteps[start_step:]  )  )

      for step, t in enumerate(self.progress_bar(self.scheduler.timesteps[start_step:]  )  ):
         if isinstance(self.unet      ,    lowercase_  ):
            _lowercase      :				Optional[Any]      					=       self.unet(lowercase_      ,    lowercase_      ,    lowercase_  )["sample"]
         else:
            _lowercase      :				Optional[Any]      					=       self.unet(lowercase_      ,    lowercase_  )["sample"]

         if isinstance(self.scheduler      ,    lowercase_  ):
            _lowercase      :				Tuple      					=       self.scheduler.step(
                model_output=lowercase_      ,    timestep=lowercase_      ,    sample=lowercase_      ,    eta=lowercase_      ,    generator=lowercase_      ,    )["prev_sample"]
         else:
            _lowercase      :				Union[str, Any]      					=       self.scheduler.step(
                model_output=lowercase_      ,    timestep=lowercase_      ,    sample=lowercase_      ,    generator=lowercase_      ,    )["prev_sample"]

         if mask is not None:
            if mask_start > 0:
               _lowercase      :				List[Any]      					=       mask[:, step, :, :mask_start]
            if mask_end > 0:
               _lowercase      :				Dict      					=       mask[:, step, :, -mask_end:]

      if self.vqvae is not None:
         # 0.18215 was scaling factor used in training to ensure unit variance
         _lowercase      :				int      					=       1 / self.vqvae.config.scaling_factor * images
         _lowercase      :				Tuple      					=       self.vqvae.decode(lowercase_  )["sample"]

      _lowercase      :				int      					=       (images / 2 + 0.5).clamp(0      ,    1  )
      _lowercase      :				Tuple      					=       images.cpu().permute(0      ,    2      ,    3      ,    1  ).numpy()
      _lowercase      :				int      					=       (images * 255).round().astype("uint8"  )
      _lowercase      :				Union[str, Any]      					=       list(
          (Image.fromarray(_[:, :, 0]  ) for _ in images)
          if images.shape[3] == 1
          else (Image.fromarray(lowercase_      ,    mode="RGB"  ).convert("L"  ) for _ in images)  )

      _lowercase      :				List[str]      					=       [self.mel.image_to_audio(lowercase_  ) for _ in images]
      if not return_dict:
         return images, (self.mel.get_sample_rate(), audios)

      return BaseOutput(**AudioPipelineOutput(np.array(lowercase_  )[:, np.newaxis, :]  )      ,    **ImagePipelineOutput(lowercase_  )  )


   @torch.no_grad()
   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase      ,    _UpperCamelCase = 50  ):





      """simple docstring"""





      assert isinstance(self.scheduler      ,    lowercase_  )
      self.scheduler.set_timesteps(lowercase_  )
      _lowercase      :				Union[str, Any]      					=       np.array(
          [np.frombuffer(image.tobytes()      ,    dtype="uint8"  ).reshape((1, image.height, image.width)  ) for image in images]  )
      _lowercase      :				List[str]      					=       (sample / 255) * 2 - 1
      _lowercase      :				List[Any]      					=       torch.Tensor(lowercase_  ).to(self.device  )

      for t in self.progress_bar(torch.flip(self.scheduler.timesteps      ,    (0,)  )  ):
         _lowercase      :				int      					=       t - self.scheduler.config.num_train_timesteps // self.scheduler.num_inference_steps
         _lowercase      :				Any      					=       self.scheduler.alphas_cumprod[t]
         _lowercase      :				Dict      					=       (
             self.scheduler.alphas_cumprod[prev_timestep]
             if prev_timestep >= 0
             else self.scheduler.final_alpha_cumprod
         )
         _lowercase      :				Any      					=       1 - alpha_prod_t
         _lowercase      :				List[Any]      					=       self.unet(lowercase_      ,    lowercase_  )["sample"]
         _lowercase      :				Optional[Any]      					=       (1 - alpha_prod_t_prev) ** 0.5 * model_output
         _lowercase      :				Any      					=       (sample - pred_sample_direction) * alpha_prod_t_prev ** (-0.5)
         _lowercase      :				List[str]      					=       sample * alpha_prod_t ** 0.5 + beta_prod_t ** 0.5 * model_output

      return sample






   @staticmethod
   def 						_lowerCamelCase       (			_UpperCamelCase      ,    _UpperCamelCase      ,    _UpperCamelCase  ):





      """simple docstring"""





      _lowercase      :				List[Any]      					=       acos(torch.dot(torch.flatten(lowercase_  )      ,    torch.flatten(lowercase_  )  ) / torch.norm(lowercase_  ) / torch.norm(lowercase_  )  )
      return sin((1 - alpha) * theta  ) * xa / sin(lowercase_  ) + sin(alpha * theta  ) * xa / sin(lowercase_  )









'''simple docstring'''
from math import sqrt







def  _A		(     snake_case					)      ->     int:
   _lowercase      :				str      					=       0
   for i in range(1		,							int(sqrt(snake_case					) + 1					)					):
      if n % i == 0 and i != sqrt(snake_case					):
         total += i + n // i
      elif i == sqrt(snake_case					):
         total += i
   return total - n







def  _A		(     snake_case = 1_00_00					)      ->     int:
   _lowercase      :				List[Any]      					=       sum(
       i
       for i in range(1		,							snake_case					)
       if sum_of_divisors(sum_of_divisors(snake_case					)					) == i and sum_of_divisors(snake_case					) != i					)
   return total


if __name__ == "__main__":
    print(solution(int(str(input()).strip())))






