






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    _lowerCAmelCase			(		lowercase_      ):



				"""simple docstring"""



				_lowercase				:   torch.FloatTensor
				_lowercase				:   torch.FloatTensor
				_lowercase				:   Optional[torch.FloatTensor]      =					None


class    _lowerCAmelCase			(		lowercase_     ,      lowercase_      ):



				"""simple docstring"""



				_lowercase				:   List[Any]      =					2



				@register_to_config
				def __init__(      self    :    Any			,		UpperCamelCase__    :    float = 0.02			,		UpperCamelCase__    :    float = 1_0_0			,		UpperCamelCase__    :    float = 1.0_07			,		UpperCamelCase__    :    float = 8_0			,		UpperCamelCase__    :    float = 0.05			,		UpperCamelCase__    :    float = 5_0			,		):






											'''simple docstring'''







											snake_case__	  =       sigma_max

											# setable values
											snake_case__	  =       None
											snake_case__	  =       None
											snake_case__	  =       None  # sigma(t_i)



				def 					__magic_name__							(      self    :    Tuple			,		UpperCamelCase__    :    torch.FloatTensor			,		UpperCamelCase__    :    Optional[int] = None):






											'''simple docstring'''







											return sample



				def 					__magic_name__							(      self    :    int			,		UpperCamelCase__    :    int			,		UpperCamelCase__    :    Union[str, torch.device] = None):






											'''simple docstring'''







											snake_case__	  =       num_inference_steps
											snake_case__	  =       np.arange(0			,		self.num_inference_steps)[::-1].copy()
											snake_case__	  =       torch.from_numpy(UpperCamelCase__).to(UpperCamelCase__)
											snake_case__	  =       [
											    (
											        self.config.sigma_max**2
											        * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
											    )
											    for i in self.timesteps
											]
											snake_case__	  =       torch.tensor(UpperCamelCase__			,		dtype=torch.floataa			,		device=UpperCamelCase__)



				def 					__magic_name__							(      self    :    List[Any]			,		UpperCamelCase__    :    torch.FloatTensor			,		UpperCamelCase__    :    float			,		UpperCamelCase__    :    Optional[torch.Generator] = None):






											'''simple docstring'''







											if self.config.s_min <= sigma <= self.config.s_max:
																		snake_case__	  =       min(self.config.s_churn / self.num_inference_steps			,		2**0.5 - 1)
											else:
																		snake_case__	  =       0

											# sample eps ~ N(0, S_noise^2 * I)
											snake_case__	  =       self.config.s_noise * randn_tensor(sample.shape			,		generator=UpperCamelCase__).to(sample.device)
											snake_case__	  =       sigma + gamma * sigma
											snake_case__	  =       sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

											return sample_hat, sigma_hat



				def 					__magic_name__							(      self    :    Any			,		UpperCamelCase__    :    torch.FloatTensor			,		UpperCamelCase__    :    float			,		UpperCamelCase__    :    float			,		UpperCamelCase__    :    torch.FloatTensor			,		UpperCamelCase__    :    bool = True			,		):






											'''simple docstring'''







											snake_case__	  =       sample_hat + sigma_hat * model_output
											snake_case__	  =       (sample_hat - pred_original_sample) / sigma_hat
											snake_case__	  =       sample_hat + (sigma_prev - sigma_hat) * derivative

											if not return_dict:
																		return (sample_prev, derivative)

											return KarrasVeOutput(
											    prev_sample=UpperCamelCase__			,		derivative=UpperCamelCase__			,		pred_original_sample=UpperCamelCase__)



				def 					__magic_name__							(      self    :    Union[str, Any]			,		UpperCamelCase__    :    torch.FloatTensor			,		UpperCamelCase__    :    float			,		UpperCamelCase__    :    float			,		UpperCamelCase__    :    torch.FloatTensor			,		UpperCamelCase__    :    torch.FloatTensor			,		UpperCamelCase__    :    torch.FloatTensor			,		UpperCamelCase__    :    bool = True			,		):






											'''simple docstring'''







											snake_case__	  =       sample_prev + sigma_prev * model_output
											snake_case__	  =       (sample_prev - pred_original_sample) / sigma_prev
											snake_case__	  =       sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

											if not return_dict:
																		return (sample_prev, derivative)

											return KarrasVeOutput(
											    prev_sample=UpperCamelCase__			,		derivative=UpperCamelCase__			,		pred_original_sample=UpperCamelCase__)



				def 					__magic_name__							(      self    :    Any			,		UpperCamelCase__    :    str			,		UpperCamelCase__    :    Optional[Any]			,		UpperCamelCase__    :    Optional[int]):






											'''simple docstring'''







											raise NotImplementedError()








def _UpperCAmelCase   (	a						:	int = 1000 ):
							snake_case__  , snake_case__	  =       1, 1
							snake_case__	  =       2
							while True:
														snake_case__	  =       0
														snake_case__	  =       fa + fa
														snake_case__  , snake_case__	  =       fa, f
														index += 1
														for _ in str(a ):
																					i += 1
														if i == n:
																					break
							return index


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