





import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput





def      _UpperCamelCase  (a__ :Dict ,      a__ :Any=0.999 ,      a__ :Optional[Any]="cosine" ,      ):






							"""simple docstring"""





							if alpha_transform_type == "cosine":

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

							elif alpha_transform_type == "exp":

														def alpha_bar_fn(a__ :Optional[Any]							):
																					return math.exp(t * -12.0							)

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

							UpperCamelCase__					  =      []
							for i in range(a__							):
														UpperCamelCase__					  =      i / num_diffusion_timesteps
														UpperCamelCase__					  =      (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 							__SCREAMING_SNAKE_CASE       (  _a ,		_a							):
							snake_case  :   Dict      =							[e.name for e in KarrasDiffusionSchedulers]
							snake_case  :   List[Any]      =							2






							@register_to_config
							def __init__(    self	,			__lowerCAmelCase = 1000	,			__lowerCAmelCase = 0.0_0085	,			__lowerCAmelCase = 0.012	,			__lowerCAmelCase = "linear"	,			__lowerCAmelCase = None	,			__lowerCAmelCase = "epsilon"	,			__lowerCAmelCase = False	,			__lowerCAmelCase = False	,			__lowerCAmelCase = 1.0	,			__lowerCAmelCase = "linspace"	,			__lowerCAmelCase = 0	,			):
														if trained_betas is not None:
																					UpperCamelCase__					  =      torch.tensor(__lowerCAmelCase	,			dtype=torch.floataa	)
														elif beta_schedule == "linear":
																					UpperCamelCase__					  =      torch.linspace(__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase	,			dtype=torch.floataa	)
														elif beta_schedule == "scaled_linear":
																					# this schedule is very specific to the latent diffusion model.
																					UpperCamelCase__					  =      (
																					    torch.linspace(beta_start**0.5	,			beta_end**0.5	,			__lowerCAmelCase	,			dtype=torch.floataa	) ** 2
																					)
														elif beta_schedule == "squaredcos_cap_v2":
																					# Glide cosine schedule
																					UpperCamelCase__					  =      betas_for_alpha_bar(__lowerCAmelCase	,			alpha_transform_type="""cosine"""	)
														elif beta_schedule == "exp":
																					UpperCamelCase__					  =      betas_for_alpha_bar(__lowerCAmelCase	,			alpha_transform_type="""exp"""	)
														else:
																					raise NotImplementedError(f"""{beta_schedule} does is not implemented for {self.__class__}"""	)

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

														#  set all values
														self.set_timesteps(__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase	)
														UpperCamelCase__					  =      use_karras_sigmas






							def 					_lowerCamelCase		(    self	,			__lowerCAmelCase	,			__lowerCAmelCase=None	):
														if schedule_timesteps is None:
																					UpperCamelCase__					  =      self.timesteps

														UpperCamelCase__					  =      (schedule_timesteps == timestep).nonzero()

														# The sigma index that is taken for the **very** first `step`
														# is always the second index (or the last index if there is only 1)
														# This way we can ensure we don't accidentally skip a sigma in
														# case we start in the middle of the denoising schedule (e.g. for image-to-image)
														if len(self._index_counter	) == 0:
																					UpperCamelCase__					  =      1 if len(__lowerCAmelCase	) > 1 else 0
														else:
																					UpperCamelCase__					  =      timestep.cpu().item() if torch.is_tensor(__lowerCAmelCase	) else timestep
																					UpperCamelCase__					  =      self._index_counter[timestep_int]

														return indices[pos].item()






							@property
							def 					_lowerCamelCase		(    self	):
														# standard deviation of the initial noise distribution
														if self.config.timestep_spacing in ["linspace", "trailing"]:
																					return self.sigmas.max()

														return (self.sigmas.max() ** 2 + 1) ** 0.5






							def 					_lowerCamelCase		(    self	,			__lowerCAmelCase	,			__lowerCAmelCase	,			):
														UpperCamelCase__					  =      self.index_for_timestep(__lowerCAmelCase	)

														UpperCamelCase__					  =      self.sigmas[step_index]
														UpperCamelCase__					  =      sample / ((sigma**2 + 1) ** 0.5)
														return sample






							def 					_lowerCamelCase		(    self	,			__lowerCAmelCase	,			__lowerCAmelCase = None	,			__lowerCAmelCase = None	,			):
														UpperCamelCase__					  =      num_inference_steps

														UpperCamelCase__					  =      num_train_timesteps or self.config.num_train_timesteps

														# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
														if self.config.timestep_spacing == "linspace":
																					UpperCamelCase__					  =      np.linspace(0	,			num_train_timesteps - 1	,			__lowerCAmelCase	,			dtype=__lowerCAmelCase	)[::-1].copy()
														elif self.config.timestep_spacing == "leading":
																					UpperCamelCase__					  =      num_train_timesteps // self.num_inference_steps
																					# creates integer timesteps by multiplying by ratio
																					# casting to int to avoid issues when num_inference_step is power of 3
																					UpperCamelCase__					  =      (np.arange(0	,			__lowerCAmelCase	) * step_ratio).round()[::-1].copy().astype(__lowerCAmelCase	)
																					timesteps += self.config.steps_offset
														elif self.config.timestep_spacing == "trailing":
																					UpperCamelCase__					  =      num_train_timesteps / self.num_inference_steps
																					# creates integer timesteps by multiplying by ratio
																					# casting to int to avoid issues when num_inference_step is power of 3
																					UpperCamelCase__					  =      (np.arange(__lowerCAmelCase	,			0	,			-step_ratio	)).round().copy().astype(__lowerCAmelCase	)
																					timesteps -= 1
														else:
																					raise ValueError(
																					    f"""{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."""	)

														UpperCamelCase__					  =      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5	)
														UpperCamelCase__					  =      np.log(__lowerCAmelCase	)
														UpperCamelCase__					  =      np.interp(__lowerCAmelCase	,			np.arange(0	,			len(__lowerCAmelCase	)	)	,			__lowerCAmelCase	)

														if self.config.use_karras_sigmas:
																					UpperCamelCase__					  =      self._convert_to_karras(in_sigmas=__lowerCAmelCase	,			num_inference_steps=self.num_inference_steps	)
																					UpperCamelCase__					  =      np.array([self._sigma_to_t(__lowerCAmelCase	,			__lowerCAmelCase	) for sigma in sigmas]	)

														UpperCamelCase__					  =      np.concatenate([sigmas, [0.0]]	).astype(np.floataa	)
														UpperCamelCase__					  =      torch.from_numpy(__lowerCAmelCase	).to(device=__lowerCAmelCase	)
														UpperCamelCase__					  =      torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2	), sigmas[-1:]]	)

														UpperCamelCase__					  =      torch.from_numpy(__lowerCAmelCase	)
														UpperCamelCase__					  =      torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2	)]	)

														if str(__lowerCAmelCase	).startswith("""mps"""	):
																					# mps does not support float64
																					UpperCamelCase__					  =      timesteps.to(__lowerCAmelCase	,			dtype=torch.floataa	)
														else:
																					UpperCamelCase__					  =      timesteps.to(device=__lowerCAmelCase	)

														# empty dt and derivative
														UpperCamelCase__					  =      None
														UpperCamelCase__					  =      None

														# for exp beta schedules, such as the one for `pipeline_shap_e.py`
														# we need an index counter
														UpperCamelCase__					  =      defaultdict(__lowerCAmelCase	)






							def 					_lowerCamelCase		(    self	,			__lowerCAmelCase	,			__lowerCAmelCase	):
														# get log sigma
														UpperCamelCase__					  =      np.log(__lowerCAmelCase	)

														# get distribution
														UpperCamelCase__					  =      log_sigma - log_sigmas[:, np.newaxis]

														# get sigmas range
														UpperCamelCase__					  =      np.cumsum((dists >= 0)	,			axis=0	).argmax(axis=0	).clip(max=log_sigmas.shape[0] - 2	)
														UpperCamelCase__					  =      low_idx + 1

														UpperCamelCase__					  =      log_sigmas[low_idx]
														UpperCamelCase__					  =      log_sigmas[high_idx]

														# interpolate sigmas
														UpperCamelCase__					  =      (low - log_sigma) / (low - high)
														UpperCamelCase__					  =      np.clip(__lowerCAmelCase	,			0	,			1	)

														# transform interpolation to time range
														UpperCamelCase__					  =      (1 - w) * low_idx + w * high_idx
														UpperCamelCase__					  =      t.reshape(sigma.shape	)
														return t






							def 					_lowerCamelCase		(    self	,			__lowerCAmelCase	,			__lowerCAmelCase	):
														UpperCamelCase__					  =      in_sigmas[-1].item()
														UpperCamelCase__					  =      in_sigmas[0].item()

														UpperCamelCase__					  =      7.0  # 7.0 is the value used in the paper
														UpperCamelCase__					  =      np.linspace(0	,			1	,			__lowerCAmelCase	)
														UpperCamelCase__					  =      sigma_min ** (1 / rho)
														UpperCamelCase__					  =      sigma_max ** (1 / rho)
														UpperCamelCase__					  =      (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
														return sigmas






							@property
							def 					_lowerCamelCase		(    self	):
														return self.dt is None






							def 					_lowerCamelCase		(    self	,			__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase = True	,			):
														UpperCamelCase__					  =      self.index_for_timestep(__lowerCAmelCase	)

														# advance index counter by 1
														UpperCamelCase__					  =      timestep.cpu().item() if torch.is_tensor(__lowerCAmelCase	) else timestep
														self._index_counter[timestep_int] += 1

														if self.state_in_first_order:
																					UpperCamelCase__					  =      self.sigmas[step_index]
																					UpperCamelCase__					  =      self.sigmas[step_index + 1]
														else:
																					# 2nd order / Heun's method
																					UpperCamelCase__					  =      self.sigmas[step_index - 1]
																					UpperCamelCase__					  =      self.sigmas[step_index]

														# currently only gamma=0 is supported. This usually works best anyways.
														# We can support gamma in the future but then need to scale the timestep before
														# passing it to the model which requires a change in API
														UpperCamelCase__					  =      0
														UpperCamelCase__					  =      sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

														# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
														if self.config.prediction_type == "epsilon":
																					UpperCamelCase__					  =      sigma_hat if self.state_in_first_order else sigma_next
																					UpperCamelCase__					  =      sample - sigma_input * model_output
														elif self.config.prediction_type == "v_prediction":
																					UpperCamelCase__					  =      sigma_hat if self.state_in_first_order else sigma_next
																					UpperCamelCase__					  =      model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
																					    sample / (sigma_input**2 + 1)
																					)
														elif self.config.prediction_type == "sample":
																					UpperCamelCase__					  =      model_output
														else:
																					raise ValueError(
																					    f"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"""	)

														if self.config.clip_sample:
																					UpperCamelCase__					  =      pred_original_sample.clamp(
																					    -self.config.clip_sample_range	,			self.config.clip_sample_range	)

														if self.state_in_first_order:
																					# 2. Convert to an ODE derivative for 1st order
																					UpperCamelCase__					  =      (sample - pred_original_sample) / sigma_hat
																					# 3. delta timestep
																					UpperCamelCase__					  =      sigma_next - sigma_hat

																					# store for 2nd order step
																					UpperCamelCase__					  =      derivative
																					UpperCamelCase__					  =      dt
																					UpperCamelCase__					  =      sample
														else:
																					# 2. 2nd order / Heun's method
																					UpperCamelCase__					  =      (sample - pred_original_sample) / sigma_next
																					UpperCamelCase__					  =      (self.prev_derivative + derivative) / 2

																					# 3. take prev timestep & sample
																					UpperCamelCase__					  =      self.dt
																					UpperCamelCase__					  =      self.sample

																					# free dt and derivative
																					# Note, this puts the scheduler in "first order mode"
																					UpperCamelCase__					  =      None
																					UpperCamelCase__					  =      None
																					UpperCamelCase__					  =      None

														UpperCamelCase__					  =      sample + derivative * dt

														if not return_dict:
																					return (prev_sample,)

														return SchedulerOutput(prev_sample=__lowerCAmelCase	)






							def 					_lowerCamelCase		(    self	,			__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase	,			):
														# Make sure sigmas and timesteps have the same device and dtype as original_samples
														UpperCamelCase__					  =      self.sigmas.to(device=original_samples.device	,			dtype=original_samples.dtype	)
														if original_samples.device.type == "mps" and torch.is_floating_point(__lowerCAmelCase	):
																					# mps does not support float64
																					UpperCamelCase__					  =      self.timesteps.to(original_samples.device	,			dtype=torch.floataa	)
																					UpperCamelCase__					  =      timesteps.to(original_samples.device	,			dtype=torch.floataa	)
														else:
																					UpperCamelCase__					  =      self.timesteps.to(original_samples.device	)
																					UpperCamelCase__					  =      timesteps.to(original_samples.device	)

														UpperCamelCase__					  =      [self.index_for_timestep(__lowerCAmelCase	,			__lowerCAmelCase	) for t in timesteps]

														UpperCamelCase__					  =      sigmas[step_indices].flatten()
														while len(sigma.shape	) < len(original_samples.shape	):
																					UpperCamelCase__					  =      sigma.unsqueeze(-1	)

														UpperCamelCase__					  =      original_samples + noise * sigma
														return noisy_samples







							def __len__(    self	):
														return self.config.num_train_timesteps











def      _UpperCamelCase  (a__ :int = 1000							):






							"""simple docstring"""





							UpperCamelCase__					  =      2**power
							UpperCamelCase__					  =      0
							while n:
														UpperCamelCase__  ,  UpperCamelCase__					  =      r + n % 10, n // 10
							return r


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




