






'''simple docstring'''







from typing import List, Optional, Tuple, Union

import torch

from ...models import UNetaDModel
from ...schedulers import KarrasVeScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput




class 		UpperCamelCase__    (a			):




		'''simple docstring'''





		_UpperCamelCase				  =					42
		_UpperCamelCase				  =					42






		def __init__(      self   ,_lowerCAmelCase   ,_lowerCAmelCase       ):
								super().__init__()
								self.register_modules(unet=_lowerCAmelCase   ,scheduler=_lowerCAmelCase       )






		@torch.no_grad()
		def __call__(      self   ,_lowerCAmelCase = 1   ,_lowerCAmelCase = 50   ,_lowerCAmelCase = None   ,_lowerCAmelCase = "pil"   ,_lowerCAmelCase = True   ,**_lowerCAmelCase   ,):
								lowerCamelCase__         =  self.unet.config.sample_size
								lowerCamelCase__         =  (batch_size, 3, img_size, img_size)

								lowerCamelCase__         =  self.unet

								# sample x_0 ~ N(0, sigma_0^2 * I)
								lowerCamelCase__         =  randn_tensor(_lowerCAmelCase   ,generator=_lowerCAmelCase   ,device=self.device       ) * self.scheduler.init_noise_sigma

								self.scheduler.set_timesteps(_lowerCAmelCase       )

								for t in self.progress_bar(self.scheduler.timesteps       ):
														# here sigma_t == t_i from the paper
														lowerCamelCase__         =  self.scheduler.schedule[t]
														lowerCamelCase__         =  self.scheduler.schedule[t - 1] if t > 0 else 0

														# 1. Select temporarily increased noise level sigma_hat
														# 2. Add new noise to move from sample_i to sample_hat
														lowerCamelCase__       ,			lowerCamelCase__         =  self.scheduler.add_noise_to_input(_lowerCAmelCase   ,_lowerCAmelCase   ,generator=_lowerCAmelCase       )

														# 3. Predict the noise residual given the noise magnitude `sigma_hat`
														# The model inputs and output are adjusted by following eq. (213) in [1].
														lowerCamelCase__         =  (sigma_hat / 2) * model((sample_hat + 1) / 2   ,sigma_hat / 2       ).sample

														# 4. Evaluate dx/dt at sigma_hat
														# 5. Take Euler step from sigma to sigma_prev
														lowerCamelCase__         =  self.scheduler.step(_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase       )

														if sigma_prev != 0:
																				# 6. Apply 2nd order correction
																				# The model inputs and output are adjusted by following eq. (213) in [1].
																				lowerCamelCase__         =  (sigma_prev / 2) * model((step_output.prev_sample + 1) / 2   ,sigma_prev / 2       ).sample
																				lowerCamelCase__         =  self.scheduler.step_correct(
																				    _lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,step_output.prev_sample   ,step_output["""derivative"""]   ,)
														lowerCamelCase__         =  step_output.prev_sample

								lowerCamelCase__         =  (sample / 2 + 0.5).clamp(0   ,1       )
								lowerCamelCase__         =  sample.cpu().permute(0   ,2   ,3   ,1       ).numpy()
								if output_type == "pil":
														lowerCamelCase__         =  self.numpy_to_pil(_lowerCAmelCase       )

								if not return_dict:
														return (image,)

								return ImagePipelineOutput(images=_lowerCAmelCase       )









'''simple docstring'''







from math import factorial

UpperCamelCase    :      dict[str, int]  			=		{str(digit): factorial(digit) for digit in range(10)}
def 						A__			(				__lowerCAmelCase		:			int						):
						if not isinstance(__lowerCAmelCase   ,    __lowerCAmelCase						):
												raise TypeError("""Parameter number must be int"""						)

						if number < 0:
												raise ValueError("""Parameter number must be greater than or equal to 0"""						)

						# Converts number in string to iterate on its digits and adds its factorial.
						return sum(DIGIT_FACTORIAL[digit] for digit in str(__lowerCAmelCase						)						)
def 						A__			(				__lowerCAmelCase		:			int = 60   ,    __lowerCAmelCase		:			int = 100_0000						):

						if not isinstance(__lowerCAmelCase   ,    __lowerCAmelCase						) or not isinstance(__lowerCAmelCase   ,    __lowerCAmelCase						):
												raise TypeError("""Parameters chain_length and number_limit must be int"""						)

						if chain_length <= 0 or number_limit <= 0:
												raise ValueError(
												    """Parameters chain_length and number_limit must be greater than 0"""						)

						# the counter for the chains with the exact desired length
						lowerCamelCase__         =  0
						# the cached sizes of the previous chains
						lowerCamelCase__         =  {}

						for start_chain_element in range(1   ,    __lowerCAmelCase						):
												# The temporary set will contain the elements of the chain
												lowerCamelCase__         =  set()
												lowerCamelCase__         =  0

												# Stop computing the chain when you find a cached size, a repeating item or the
												# length is greater then the desired one.
												lowerCamelCase__         =  start_chain_element
												while (
												    chain_element not in chain_sets_lengths
												    and chain_element not in chain_set
												    and chain_set_length <= chain_length
												):
																		chain_set.add(__lowerCAmelCase						)
																		chain_set_length += 1
																		lowerCamelCase__         =  digit_factorial_sum(__lowerCAmelCase						)

												if chain_element in chain_sets_lengths:
																		chain_set_length += chain_sets_lengths[chain_element]

												lowerCamelCase__         =  chain_set_length

												# If chain contains the exact amount of elements increase the counter
												if chain_set_length == chain_length:
																		chains_counter += 1

						return chains_counter


if __name__ == "__main__":
							import doctest

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

