
import importlib
import math
import os
from dataclasses import dataclass
from enum import Enum
from typing import Any, Dict, Optional, Tuple, Union

import flax
import jax.numpy as jnp

from ..utils import BaseOutput


lowercase  : str						   =							"""scheduler_config.json"""

class __snake_case		(				lowerCAmelCase					):
    _a		:						Any=    1
    _a		:						List[str]=    2
    _a		:						List[Any]=    3
    _a		:						List[Any]=    4
    _a		:						List[str]=    5






@dataclass
class __snake_case		(				lowerCAmelCase					):
    _a		:						jnp.ndarray






class __snake_case		:
    _a		:						Dict=    SCHEDULER_CONFIG_NAME
    _a		:						Any=    ["dtype"]
    _a		:						List[Any]=    []
    _a		:						List[Any]=    True
    @classmethod
    def 				_SCREAMING_SNAKE_CASE	(  cls		,snake_case = None		,snake_case = None		,snake_case=False		,**snake_case		,):



           '''simple docstring'''







           lowercase     ,      lowercase							:					Optional[int]	     =				cls.load_config(
               pretrained_model_name_or_path=snake_case		,subfolder=snake_case		,return_unused_kwargs=snake_case		,**snake_case		,)
           lowercase     ,      lowercase							:					List[str]	     =				cls.from_config(snake_case		,return_unused_kwargs=snake_case		,**snake_case				)

           if hasattr(snake_case		,"""create_state"""				) and getattr(snake_case		,"""has_state"""		,snake_case				):
                  lowercase							:					Optional[Any]	     =				scheduler.create_state()

           if return_unused_kwargs:
                  return scheduler, state, unused_kwargs

           return scheduler, state
    def 				_SCREAMING_SNAKE_CASE	(  self		,snake_case		,snake_case = False		,**snake_case				):



           '''simple docstring'''







           self.save_config(save_directory=snake_case		,push_to_hub=snake_case		,**snake_case				)
    @property
    def 				_SCREAMING_SNAKE_CASE	(  self				):



           '''simple docstring'''







           return self._get_compatibles()
    @classmethod
    def 				_SCREAMING_SNAKE_CASE	(  cls				):



           '''simple docstring'''







           lowercase							:					Optional[int]	     =				list(set([cls.__name__] + cls._compatibles				)				)
           lowercase							:					Union[str, Any]	     =				importlib.import_module(__name__.split("""."""				)[0]				)
           lowercase							:					Tuple	     =				[
               getattr(snake_case		,snake_case				) for c in compatible_classes_str if hasattr(snake_case		,snake_case				)
           ]
           return compatible_classes







def 						_snake_case(  SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__    )			->   jnp.ndarray:
       assert len(SCREAMING_SNAKE_CASE__    ) >= x.ndim
       return jnp.broadcast_to(x.reshape(x.shape + (1,) * (len(SCREAMING_SNAKE_CASE__    ) - x.ndim)    ) ,     SCREAMING_SNAKE_CASE__    )







def 						_snake_case(  SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__=0.999 ,     SCREAMING_SNAKE_CASE__=jnp.floataa    )			->   jnp.ndarray:

       def alpha_bar(SCREAMING_SNAKE_CASE__    ):
              return math.cos((time_step + 0.008) / 1.008 * math.pi / 2    ) ** 2

       lowercase							:					Dict	     =				[]
       for i in range(SCREAMING_SNAKE_CASE__    ):
              lowercase							:					Tuple	     =				i / num_diffusion_timesteps
              lowercase							:					List[str]	     =				(i + 1) / num_diffusion_timesteps
              betas.append(min(1 - alpha_bar(SCREAMING_SNAKE_CASE__    ) / alpha_bar(SCREAMING_SNAKE_CASE__    ) ,     SCREAMING_SNAKE_CASE__    )    )
       return jnp.array(SCREAMING_SNAKE_CASE__ ,     dtype=SCREAMING_SNAKE_CASE__    )

@flax.struct.dataclass
class __snake_case		:
    _a		:						jnp.ndarray
    _a		:						jnp.ndarray
    _a		:						jnp.ndarray
    @classmethod
    def 				_SCREAMING_SNAKE_CASE	(  cls		,snake_case				):



           '''simple docstring'''







           lowercase							:					List[Any]	     =				scheduler.config

           if config.trained_betas is not None:
                  lowercase							:					List[Any]	     =				jnp.asarray(config.trained_betas		,dtype=scheduler.dtype				)
           elif config.beta_schedule == "linear":
                  lowercase							:					Any	     =				jnp.linspace(config.beta_start		,config.beta_end		,config.num_train_timesteps		,dtype=scheduler.dtype				)
           elif config.beta_schedule == "scaled_linear":
                  # this schedule is very specific to the latent diffusion model.
                  lowercase							:					str	     =				(
                      jnp.linspace(
                          config.beta_start**0.5		,config.beta_end**0.5		,config.num_train_timesteps		,dtype=scheduler.dtype				)
                      ** 2
                  )
           elif config.beta_schedule == "squaredcos_cap_v2":
                  # Glide cosine schedule
                  lowercase							:					str	     =				betas_for_alpha_bar(config.num_train_timesteps		,dtype=scheduler.dtype				)
           else:
                  raise NotImplementedError(
                      f"beta_schedule {config.beta_schedule} is not implemented for scheduler {scheduler.__class__.__name__}"				)

           lowercase							:					int	     =				1.0 - betas

           lowercase							:					Optional[Any]	     =				jnp.cumprod(snake_case		,axis=0				)

           return cls(
               alphas=snake_case		,betas=snake_case		,alphas_cumprod=snake_case		,)







def 						_snake_case(  SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__    )			->   Any:
       lowercase							:					Tuple	     =				state.alphas_cumprod

       lowercase							:					Any	     =				alphas_cumprod[timesteps] ** 0.5
       lowercase							:					List[Any]	     =				sqrt_alpha_prod.flatten()
       lowercase							:					Optional[Any]	     =				broadcast_to_shape_from_left(SCREAMING_SNAKE_CASE__ ,     original_samples.shape    )

       lowercase							:					str	     =				(1 - alphas_cumprod[timesteps]) ** 0.5
       lowercase							:					Union[str, Any]	     =				sqrt_one_minus_alpha_prod.flatten()
       lowercase							:					List[str]	     =				broadcast_to_shape_from_left(SCREAMING_SNAKE_CASE__ ,     original_samples.shape    )

       return sqrt_alpha_prod, sqrt_one_minus_alpha_prod







def 						_snake_case(  SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__    )			->   Any:
       lowercase     ,      lowercase							:					Union[str, Any]	     =				get_sqrt_alpha_prod(SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__    )
       lowercase							:					Tuple	     =				sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
       return noisy_samples







def 						_snake_case(  SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__    )			->   str:
       lowercase     ,      lowercase							:					List[Any]	     =				get_sqrt_alpha_prod(SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__    )
       lowercase							:					Any	     =				sqrt_alpha_prod * noise - sqrt_one_minus_alpha_prod * sample
       return velocity


from collections.abc import Generator







def 						_snake_case(  )			->   Generator[int, None, None]:
       lowercase     ,      lowercase							:					List[str]	     =				0, 1
       while True:
              lowercase     ,      lowercase							:					Optional[int]	     =				b, a + b
              yield b







def 						_snake_case(  SCREAMING_SNAKE_CASE__ = 1_000    )			->   int:
       lowercase							:					List[Any]	     =				1
       lowercase							:					Tuple	     =				fibonacci_generator()
       while len(str(next(SCREAMING_SNAKE_CASE__    )    )    ) < n:
              answer += 1
       return answer + 1


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