






'''simple docstring'''







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 		UpperCamelCase__    :




		'''simple docstring'''





		_UpperCamelCase				  =					None
		_UpperCamelCase				  =					None
		_UpperCamelCase				  =					None  # sigma(t_i)






		@classmethod
		def 			UpperCamelCase_					(      cls       ):
								return cls()




@dataclass
class 		UpperCamelCase__    (a			):




		'''simple docstring'''





		_UpperCamelCase				  =					42
		_UpperCamelCase				  =					42
		_UpperCamelCase				  =					42




class 		UpperCamelCase__    (a   ,a			):




		'''simple docstring'''





		@property
		def 			UpperCamelCase_					(      self       ):
								return True






		@register_to_config
		def __init__(      self   ,_lowerCAmelCase = 0.02   ,_lowerCAmelCase = 1_00   ,_lowerCAmelCase = 1.007   ,_lowerCAmelCase = 80   ,_lowerCAmelCase = 0.05   ,_lowerCAmelCase = 50   ,):
								pass






		def 			UpperCamelCase_					(      self       ):
								return KarrasVeSchedulerState.create()






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase = ()       ):
								lowerCamelCase__         =  jnp.arange(0   ,_lowerCAmelCase       )[::-1].copy()
								lowerCamelCase__         =  [
								    (
								        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=_lowerCAmelCase   ,schedule=jnp.array(_lowerCAmelCase   ,dtype=jnp.floataa       )   ,timesteps=_lowerCAmelCase   ,)






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

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

								return sample_hat, sigma_hat






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase = True   ,):
								lowerCamelCase__         =  sample_hat + sigma_hat * model_output
								lowerCamelCase__         =  (sample_hat - pred_original_sample) / sigma_hat
								lowerCamelCase__         =  sample_hat + (sigma_prev - sigma_hat) * derivative

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

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






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase = True   ,):
								lowerCamelCase__         =  sample_prev + sigma_prev * model_output
								lowerCamelCase__         =  (sample_prev - pred_original_sample) / sigma_prev
								lowerCamelCase__         =  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=_lowerCAmelCase   ,derivative=_lowerCAmelCase   ,state=_lowerCAmelCase       )






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase       ):
								raise NotImplementedError()









'''simple docstring'''







UpperCamelCase    :      Tuple  			=		[sum(int(c, 10) ** 2 for c in i.__str__()) for i in range(10_00_00)]
def 						A__			(				__lowerCAmelCase		:			int						):
						lowerCamelCase__         =  0
						while number:
												# Increased Speed Slightly by checking every 5 digits together.
												sum_of_digits_squared += DIGITS_SQUARED[number % 10_0000]
												number //= 10_0000

						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
UpperCamelCase    :      list[bool | None]  			=		[None] * 10_00_00_00
UpperCamelCase    :      Tuple  			=		True
UpperCamelCase    :      Optional[int]  			=		False
def 						A__			(				__lowerCAmelCase		:			int						):

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

						lowerCamelCase__         =  chain(next_number(__lowerCAmelCase						)						)
						lowerCamelCase__         =  number_chain

						while number < 1000_0000:
												lowerCamelCase__         =  number_chain
												number *= 10

						return number_chain
def 						A__			(				__lowerCAmelCase		:			int = 1000_0000						):
						for i in range(1   ,    __lowerCAmelCase						):
												if CHAINS[i] is None:
																		chain(i + 1						)

						return CHAINS[:number].count(__lowerCAmelCase						)


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							print(F'{solution() = }')

