


from dataclasses import dataclass
from typing import Optional, Tuple, Union

import flax
import jax.numpy as jnp
from jax import random

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils_flax import FlaxSchedulerMixin


@flax.struct.dataclass
class 	_a							:
							_lowercase     :      Tuple  				=			None
							_lowercase     :      Union[str, Any]  				=			None
							_lowercase     :      Union[str, Any]  				=			None  # sigma(t_i)

							@classmethod
							def 				lowerCamelCase_			(							cls:     Dict							)      ->       Tuple:





									"""simple docstring"""







									return cls()


@dataclass
class 	_a							(      UpperCamelCase__      ):
							_lowercase     :      Dict  				=			42
							_lowercase     :      Optional[Any]  				=			42
							_lowercase     :      Optional[int]  				=			42


class 	_a							(      UpperCamelCase__					,     UpperCamelCase__      ):

							@property
							def 				lowerCamelCase_			(							self:     Tuple							)      ->       Optional[int]:





									"""simple docstring"""







									return True

							@register_to_config
							def __init__(							self:     List[str]   ,						UpperCamelCase_:     List[str] = 0.02   ,						UpperCamelCase_:     Dict = 100   ,						UpperCamelCase_:     Union[str, Any] = 1.007   ,						UpperCamelCase_:     Any = 80   ,						UpperCamelCase_:     List[str] = 0.05   ,						UpperCamelCase_:     int = 50   ,						)      ->       Any:





									"""simple docstring"""







									pass

							def 				lowerCamelCase_			(							self:     Dict							)      ->       int:





									"""simple docstring"""







									return KarrasVeSchedulerState.create()

							def 				lowerCamelCase_			(							self:     Optional[Any]   ,						UpperCamelCase_:     Optional[Any]   ,						UpperCamelCase_:     List[Any]   ,						UpperCamelCase_:     Dict = ()							)      ->       KarrasVeSchedulerState:





									"""simple docstring"""







									lowercase__						=				jnp.arange(0   ,						UpperCamelCase_							)[::-1].copy()
									lowercase__						=				[
									    (
									        self.config.sigma_max**2
									        * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
									    )
									    for i in timesteps
									]

									return state.replace(
									    num_inference_steps=UpperCamelCase_   ,						schedule=jnp.array(UpperCamelCase_   ,						dtype=jnp.floataa							)   ,						timesteps=UpperCamelCase_   ,						)

							def 				lowerCamelCase_			(							self:     List[Any]   ,						UpperCamelCase_:     Optional[int]   ,						UpperCamelCase_:     str   ,						UpperCamelCase_:     Union[str, Any]   ,						UpperCamelCase_:     int   ,						)      ->       Tuple[jnp.ndarray, float]:





									"""simple docstring"""







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

									# sample eps ~ N(0, S_noise^2 * I)
									lowercase__						=				random.split(UpperCamelCase_   ,						num=1							)
									lowercase__						=				self.config.s_noise * random.normal(key=UpperCamelCase_   ,						shape=sample.shape							)
									lowercase__						=				sigma + gamma * sigma
									lowercase__						=				sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

									return sample_hat, sigma_hat

							def 				lowerCamelCase_			(							self:     Optional[Any]   ,						UpperCamelCase_:     Dict   ,						UpperCamelCase_:     Tuple   ,						UpperCamelCase_:     List[Any]   ,						UpperCamelCase_:     Any   ,						UpperCamelCase_:     Dict   ,						UpperCamelCase_:     List[Any] = True   ,						)      ->       Union[FlaxKarrasVeOutput, Tuple]:





									"""simple docstring"""







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

									if not return_dict:
											return (sample_prev, derivative, state)

									return FlaxKarrasVeOutput(prev_sample=UpperCamelCase_   ,						derivative=UpperCamelCase_   ,						state=UpperCamelCase_							)

							def 				lowerCamelCase_			(							self:     str   ,						UpperCamelCase_:     Optional[Any]   ,						UpperCamelCase_:     List[str]   ,						UpperCamelCase_:     int   ,						UpperCamelCase_:     Dict   ,						UpperCamelCase_:     Any   ,						UpperCamelCase_:     Any   ,						UpperCamelCase_:     Tuple   ,						UpperCamelCase_:     int = True   ,						)      ->       Union[FlaxKarrasVeOutput, Tuple]:





									"""simple docstring"""







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

									if not return_dict:
											return (sample_prev, derivative, state)

									return FlaxKarrasVeOutput(prev_sample=UpperCamelCase_   ,						derivative=UpperCamelCase_   ,						state=UpperCamelCase_							)


							def 				lowerCamelCase_			(							self:     Tuple   ,						UpperCamelCase_:     Optional[Any]   ,						UpperCamelCase_:     List[str]   ,						UpperCamelCase_:     List[Any]   ,						UpperCamelCase_:     str							)      ->       Any:





									"""simple docstring"""







									raise NotImplementedError()






lowerCAmelCase	=							[sum(int(c, 10) ** 2 for c in i.__str__()) for i in range(10_0000)]
def       _a			(				SCREAMING_SNAKE_CASE					):


		"""simple docstring"""




		lowercase__						=				0
		while number:
				# Increased Speed Slightly by checking every 5 digits together.
				sum_of_digits_squared += DIGITS_SQUARED[number % 10_00_00]
				number //= 10_00_00

		return sum_of_digits_squared


# There are 2 Chains made,
# One ends with 89 with the chain member 58 being the one which when declared first,
# there will be the least number of iterations for all the members to be checked.

# The other one ends with 1 and has only one element 1.

# So 58 and 1 are chosen to be declared at the starting.

# Changed dictionary to an array to quicken the solution
lowerCAmelCase	=							[None] * 1000_0000
lowerCAmelCase	=							True
lowerCAmelCase	=							False
def       _a			(				SCREAMING_SNAKE_CASE					):


		"""simple docstring"""




		if CHAINS[number - 1] is not None:
				return CHAINS[number - 1]  # type: ignore

		lowercase__						=				chain(next_number(SCREAMING_SNAKE_CASE					)					)
		lowercase__						=				number_chain

		while number < 10_00_00_00:
				lowercase__						=				number_chain
				number *= 10

		return number_chain
def       _a			(				SCREAMING_SNAKE_CASE = 10_00_00_00					):


		"""simple docstring"""




		for i in range(1						,    SCREAMING_SNAKE_CASE					):
				if CHAINS[i] is None:
						chain(i + 1					)

		return CHAINS[:number].count(SCREAMING_SNAKE_CASE					)


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			print(f"""{solution() = }""")


