


"""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
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->UnCLIP
class   _a      (      SCREAMING_SNAKE_CASE_ ):
    a_    :				torch.FloatTensor
    a_    :				Optional[torch.FloatTensor]             =    None





def   snake_case						(				_a:     List[str]		,   _a:     Dict=0.999		,   _a:     Union[str, Any]="cosine"		,   )->		Any:
      '''simple docstring'''


      if alpha_transform_type == "cosine":

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

      elif alpha_transform_type == "exp":

            def alpha_bar_fn(_a:     Union[str, Any]							):
                  return math.exp(t * -12.0							)

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

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






class   _a      (      SCREAMING_SNAKE_CASE_		,		SCREAMING_SNAKE_CASE_ ):
    @register_to_config
    def __init__( self							:					Union[str, Any]							,					SCREAMING_SNAKE_CASE__							:					int = 10_00							,					SCREAMING_SNAKE_CASE__							:					str = "fixed_small_log"							,					SCREAMING_SNAKE_CASE__							:					bool = True							,					SCREAMING_SNAKE_CASE__							:					Optional[float] = 1.0							,					SCREAMING_SNAKE_CASE__							:					str = "epsilon"							,					SCREAMING_SNAKE_CASE__							:					str = "squaredcos_cap_v2"							,					):
          if beta_schedule != "squaredcos_cap_v2":
                raise ValueError('UnCLIPScheduler only supports `beta_schedule`: \'squaredcos_cap_v2\''				)

          lowerCamelCase__           =		betas_for_alpha_bar(SCREAMING_SNAKE_CASE__				)

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

          # standard deviation of the initial noise distribution
          lowerCamelCase__           =		1.0

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

          lowerCamelCase__           =		variance_type
    def      _UpperCamelCase       ( self							:					Dict							,					SCREAMING_SNAKE_CASE__							:					torch.FloatTensor							,					SCREAMING_SNAKE_CASE__							:					Optional[int] = None				):
          return sample
    def      _UpperCamelCase       ( self							:					int							,					SCREAMING_SNAKE_CASE__							:					int							,					SCREAMING_SNAKE_CASE__							:					Union[str, torch.device] = None				):
          lowerCamelCase__           =		num_inference_steps
          lowerCamelCase__           =		(self.config.num_train_timesteps - 1) / (self.num_inference_steps - 1)
          lowerCamelCase__           =		(np.arange(0							,					SCREAMING_SNAKE_CASE__				) * step_ratio).round()[::-1].copy().astype(np.intaa				)
          lowerCamelCase__           =		torch.from_numpy(SCREAMING_SNAKE_CASE__				).to(SCREAMING_SNAKE_CASE__				)
    def      _UpperCamelCase       ( self							:					int							,					SCREAMING_SNAKE_CASE__							:					Optional[Any]							,					SCREAMING_SNAKE_CASE__							:					Optional[int]=None							,					SCREAMING_SNAKE_CASE__							:					Union[str, Any]=None							,					SCREAMING_SNAKE_CASE__							:					Optional[int]=None				):
          if prev_timestep is None:
                lowerCamelCase__           =		t - 1

          lowerCamelCase__           =		self.alphas_cumprod[t]
          lowerCamelCase__           =		self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
          lowerCamelCase__           =		1 - alpha_prod_t
          lowerCamelCase__           =		1 - alpha_prod_t_prev

          if prev_timestep == t - 1:
                lowerCamelCase__           =		self.betas[t]
          else:
                lowerCamelCase__           =		1 - alpha_prod_t / 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
          lowerCamelCase__           =		beta_prod_t_prev / beta_prod_t * beta

          if variance_type is None:
                lowerCamelCase__           =		self.config.variance_type

          # hacks - were probably added for training stability
          if variance_type == "fixed_small_log":
                lowerCamelCase__           =		torch.log(torch.clamp(SCREAMING_SNAKE_CASE__							,					min=1e-20				)				)
                lowerCamelCase__           =		torch.exp(0.5 * variance				)
          elif variance_type == "learned_range":
                # NOTE difference with DDPM scheduler
                lowerCamelCase__           =		variance.log()
                lowerCamelCase__           =		beta.log()

                lowerCamelCase__           =		(predicted_variance + 1) / 2
                lowerCamelCase__           =		frac * max_log + (1 - frac) * min_log

          return variance
    def      _UpperCamelCase       ( self							:					Tuple							,					SCREAMING_SNAKE_CASE__							:					torch.FloatTensor							,					SCREAMING_SNAKE_CASE__							:					int							,					SCREAMING_SNAKE_CASE__							:					torch.FloatTensor							,					SCREAMING_SNAKE_CASE__							:					Optional[int] = None							,					SCREAMING_SNAKE_CASE__							:					Tuple=None							,					SCREAMING_SNAKE_CASE__							:					bool = True							,					):
          lowerCamelCase__           =		timestep

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

          # 1. compute alphas, betas
          if prev_timestep is None:
                lowerCamelCase__           =		t - 1

          lowerCamelCase__           =		self.alphas_cumprod[t]
          lowerCamelCase__           =		self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
          lowerCamelCase__           =		1 - alpha_prod_t
          lowerCamelCase__           =		1 - alpha_prod_t_prev

          if prev_timestep == t - 1:
                lowerCamelCase__           =		self.betas[t]
                lowerCamelCase__           =		self.alphas[t]
          else:
                lowerCamelCase__           =		1 - alpha_prod_t / alpha_prod_t_prev
                lowerCamelCase__           =		1 - beta

          # 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 self.config.prediction_type == "epsilon":
                lowerCamelCase__           =		(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
          elif self.config.prediction_type == "sample":
                lowerCamelCase__           =		model_output
          else:
                raise ValueError(
                    F'prediction_type given as {self.config.prediction_type} must be one of `epsilon` or `sample`'
                    ' for the UnCLIPScheduler.'				)

          # 3. Clip "predicted x_0"
          if self.config.clip_sample:
                lowerCamelCase__           =		torch.clamp(
                    SCREAMING_SNAKE_CASE__							,					-self.config.clip_sample_range							,					self.config.clip_sample_range				)

          # 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
          lowerCamelCase__           =		(alpha_prod_t_prev ** 0.5 * beta) / beta_prod_t
          lowerCamelCase__           =		alpha ** 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
          lowerCamelCase__           =		pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

          # 6. Add noise
          lowerCamelCase__           =		0
          if t > 0:
                lowerCamelCase__           =		randn_tensor(
                    model_output.shape							,					dtype=model_output.dtype							,					generator=SCREAMING_SNAKE_CASE__							,					device=model_output.device				)

                lowerCamelCase__           =		self._get_variance(
                    SCREAMING_SNAKE_CASE__							,					predicted_variance=SCREAMING_SNAKE_CASE__							,					prev_timestep=SCREAMING_SNAKE_CASE__							,					)

                if self.variance_type == "fixed_small_log":
                      lowerCamelCase__           =		variance
                elif self.variance_type == "learned_range":
                      lowerCamelCase__           =		(0.5 * variance).exp()
                else:
                      raise ValueError(
                          F'variance_type given as {self.variance_type} must be one of `fixed_small_log` or `learned_range`'
                          ' for the UnCLIPScheduler.'				)

                lowerCamelCase__           =		variance * variance_noise

          lowerCamelCase__           =		pred_prev_sample + variance

          if not return_dict:
                return (pred_prev_sample,)

          return UnCLIPSchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE__							,					pred_original_sample=SCREAMING_SNAKE_CASE__				)


    def      _UpperCamelCase       ( self							:					Optional[Any]							,					SCREAMING_SNAKE_CASE__							:					torch.FloatTensor							,					SCREAMING_SNAKE_CASE__							:					torch.FloatTensor							,					SCREAMING_SNAKE_CASE__							:					torch.IntTensor							,					):
          # Make sure alphas_cumprod and timestep have same device and dtype as original_samples
          lowerCamelCase__           =		self.alphas_cumprod.to(device=original_samples.device							,					dtype=original_samples.dtype				)
          lowerCamelCase__           =		timesteps.to(original_samples.device				)

          lowerCamelCase__           =		alphas_cumprod[timesteps] ** 0.5
          lowerCamelCase__           =		sqrt_alpha_prod.flatten()
          while len(sqrt_alpha_prod.shape				) < len(original_samples.shape				):
                lowerCamelCase__           =		sqrt_alpha_prod.unsqueeze(-1				)

          lowerCamelCase__           =		(1 - alphas_cumprod[timesteps]) ** 0.5
          lowerCamelCase__           =		sqrt_one_minus_alpha_prod.flatten()
          while len(sqrt_one_minus_alpha_prod.shape				) < len(original_samples.shape				):
                lowerCamelCase__           =		sqrt_one_minus_alpha_prod.unsqueeze(-1				)

          lowerCamelCase__           =		sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
          return noisy_samples







"""simple docstring"""


def   snake_case						(				_a:     int							)->		int:
      '''simple docstring'''


      lowerCamelCase__           =		1
      for i in range(1		,   num + 1							):
            fact *= i
      return fact



def   snake_case						(				_a:     int							)->		int:
      '''simple docstring'''


      lowerCamelCase__           =		0
      while number > 0:
            lowerCamelCase__           =		number % 10
            sum_of_digits += last_digit
            lowerCamelCase__           =		number // 10  # Removing the last_digit from the given number
      return sum_of_digits



def   snake_case						(				_a:     int = 100							)->		int:
      '''simple docstring'''


      lowerCamelCase__           =		factorial(_a							)
      lowerCamelCase__           =		split_and_add(_a							)
      return result


if __name__ == "__main__":
   print(solution(int(input("Enter the Number: ").strip())))



