
from math import factorial

__lowerCAmelCase					   =       {str(digit): factorial(digit) for digit in range(1_0)}


def    a      ( a	)     ->int:




			'''simple docstring'''


			if not isinstance(a		,						a	):
						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(a	)	)


def    a      ( a = 60		,						a = 100_0000	)     ->int:




			'''simple docstring'''


			if not isinstance(a		,						a	) or not isinstance(a		,						a	):
						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
			SCREAMING_SNAKE_CASE     						= 0
			# the cached sizes of the previous chains
			SCREAMING_SNAKE_CASE     						= {}

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

						# Stop computing the chain when you find a cached size, a repeating item or the
						# length is greater then the desired one.
						SCREAMING_SNAKE_CASE     						= 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(a	)
									chain_set_length += 1
									SCREAMING_SNAKE_CASE     						= digit_factorial_sum(a	)

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

						SCREAMING_SNAKE_CASE     						= 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()}''')

import torch

from diffusers import DDPMParallelScheduler

from .test_schedulers import SchedulerCommonTest





class     lowerCamelCase      (       __lowerCamelCase					):
	UpperCamelCase_  :					int    		=	(DDPMParallelScheduler,)







	def  snake_case__     (     self      :Any   ,     **lowercase      :str			)		->      Any:







				"""simple docstring"""






				SCREAMING_SNAKE_CASE     						= {
				    '''num_train_timesteps''': 1_0_0_0,
				    '''beta_start''': 0.00_01,
				    '''beta_end''': 0.02,
				    '''beta_schedule''': '''linear''',
				    '''variance_type''': '''fixed_small''',
				    '''clip_sample''': True,
				}

				config.update(**lowercase			)
				return config







	def  snake_case__     (     self      :Dict			)		->      List[Any]:







				"""simple docstring"""






				for timesteps in [1, 5, 1_0_0, 1_0_0_0]:
							self.check_over_configs(num_train_timesteps=lowercase			)







	def  snake_case__     (     self      :List[Any]			)		->      Optional[Any]:







				"""simple docstring"""






				for beta_start, beta_end in zip([0.00_01, 0.0_01, 0.01, 0.1]   ,     [0.0_02, 0.02, 0.2, 2]			):
							self.check_over_configs(beta_start=lowercase   ,     beta_end=lowercase			)







	def  snake_case__     (     self      :Any			)		->      List[str]:







				"""simple docstring"""






				for schedule in ["linear", "squaredcos_cap_v2"]:
							self.check_over_configs(beta_schedule=lowercase			)







	def  snake_case__     (     self      :Optional[int]			)		->      List[str]:







				"""simple docstring"""






				for variance in ["fixed_small", "fixed_large", "other"]:
							self.check_over_configs(variance_type=lowercase			)







	def  snake_case__     (     self      :Any			)		->      List[Any]:







				"""simple docstring"""






				for clip_sample in [True, False]:
							self.check_over_configs(clip_sample=lowercase			)







	def  snake_case__     (     self      :str			)		->      str:







				"""simple docstring"""






				self.check_over_configs(thresholding=lowercase			)
				for threshold in [0.5, 1.0, 2.0]:
							for prediction_type in ["epsilon", "sample", "v_prediction"]:
										self.check_over_configs(
										    thresholding=lowercase   ,     prediction_type=lowercase   ,     sample_max_value=lowercase   ,     )







	def  snake_case__     (     self      :Union[str, Any]			)		->      List[Any]:







				"""simple docstring"""






				for prediction_type in ["epsilon", "sample", "v_prediction"]:
							self.check_over_configs(prediction_type=lowercase			)







	def  snake_case__     (     self      :List[str]			)		->      Optional[int]:







				"""simple docstring"""






				for t in [0, 5_0_0, 9_9_9]:
							self.check_over_forward(time_step=lowercase			)







	def  snake_case__     (     self      :List[Any]			)		->      Optional[int]:







				"""simple docstring"""






				SCREAMING_SNAKE_CASE     						= self.scheduler_classes[0]
				SCREAMING_SNAKE_CASE     						= self.get_scheduler_config()
				SCREAMING_SNAKE_CASE     						= scheduler_class(**lowercase			)

				assert torch.sum(torch.abs(scheduler._get_variance(0			) - 0.0			)			) < 1e-5
				assert torch.sum(torch.abs(scheduler._get_variance(4_8_7			) - 0.0_09_79			)			) < 1e-5
				assert torch.sum(torch.abs(scheduler._get_variance(9_9_9			) - 0.02			)			) < 1e-5







	def  snake_case__     (     self      :Tuple			)		->      List[str]:







				"""simple docstring"""






				SCREAMING_SNAKE_CASE     						= self.scheduler_classes[0]
				SCREAMING_SNAKE_CASE     						= self.get_scheduler_config()
				SCREAMING_SNAKE_CASE     						= scheduler_class(**lowercase			)

				SCREAMING_SNAKE_CASE     						= len(lowercase			)

				SCREAMING_SNAKE_CASE     						= self.dummy_model()
				SCREAMING_SNAKE_CASE     						= self.dummy_sample_deter
				SCREAMING_SNAKE_CASE     						= self.dummy_sample_deter + 0.1
				SCREAMING_SNAKE_CASE     						= self.dummy_sample_deter - 0.1

				SCREAMING_SNAKE_CASE     						= samplea.shape[0]
				SCREAMING_SNAKE_CASE     						= torch.stack([samplea, samplea, samplea]   ,     dim=0			)
				SCREAMING_SNAKE_CASE     						= torch.arange(lowercase			)[0:3, None].repeat(1   ,     lowercase			)

				SCREAMING_SNAKE_CASE     						= model(samples.flatten(0   ,     1			)   ,     timesteps.flatten(0   ,     1			)			)
				SCREAMING_SNAKE_CASE     						= scheduler.batch_step_no_noise(lowercase   ,     timesteps.flatten(0   ,     1			)   ,     samples.flatten(0   ,     1			)			)

				SCREAMING_SNAKE_CASE     						= torch.sum(torch.abs(lowercase			)			)
				SCREAMING_SNAKE_CASE     						= torch.mean(torch.abs(lowercase			)			)

				assert abs(result_sum.item() - 11_53.18_33			) < 1e-2
				assert abs(result_mean.item() - 0.50_05			) < 1e-3







	def  snake_case__     (     self      :str			)		->      List[Any]:







				"""simple docstring"""






				SCREAMING_SNAKE_CASE     						= self.scheduler_classes[0]
				SCREAMING_SNAKE_CASE     						= self.get_scheduler_config()
				SCREAMING_SNAKE_CASE     						= scheduler_class(**lowercase			)

				SCREAMING_SNAKE_CASE     						= len(lowercase			)

				SCREAMING_SNAKE_CASE     						= self.dummy_model()
				SCREAMING_SNAKE_CASE     						= self.dummy_sample_deter
				SCREAMING_SNAKE_CASE     						= torch.manual_seed(0			)

				for t in reversed(range(lowercase			)			):
							# 1. predict noise residual
							SCREAMING_SNAKE_CASE     						= model(lowercase   ,     lowercase			)

							# 2. predict previous mean of sample x_t-1
							SCREAMING_SNAKE_CASE     						= scheduler.step(lowercase   ,     lowercase   ,     lowercase   ,     generator=lowercase			).prev_sample

							SCREAMING_SNAKE_CASE     						= pred_prev_sample

				SCREAMING_SNAKE_CASE     						= torch.sum(torch.abs(lowercase			)			)
				SCREAMING_SNAKE_CASE     						= torch.mean(torch.abs(lowercase			)			)

				assert abs(result_sum.item() - 2_58.96_06			) < 1e-2
				assert abs(result_mean.item() - 0.33_72			) < 1e-3







	def  snake_case__     (     self      :int			)		->      str:







				"""simple docstring"""






				SCREAMING_SNAKE_CASE     						= self.scheduler_classes[0]
				SCREAMING_SNAKE_CASE     						= self.get_scheduler_config(prediction_type='''v_prediction'''			)
				SCREAMING_SNAKE_CASE     						= scheduler_class(**lowercase			)

				SCREAMING_SNAKE_CASE     						= len(lowercase			)

				SCREAMING_SNAKE_CASE     						= self.dummy_model()
				SCREAMING_SNAKE_CASE     						= self.dummy_sample_deter
				SCREAMING_SNAKE_CASE     						= torch.manual_seed(0			)

				for t in reversed(range(lowercase			)			):
							# 1. predict noise residual
							SCREAMING_SNAKE_CASE     						= model(lowercase   ,     lowercase			)

							# 2. predict previous mean of sample x_t-1
							SCREAMING_SNAKE_CASE     						= scheduler.step(lowercase   ,     lowercase   ,     lowercase   ,     generator=lowercase			).prev_sample

							SCREAMING_SNAKE_CASE     						= pred_prev_sample

				SCREAMING_SNAKE_CASE     						= torch.sum(torch.abs(lowercase			)			)
				SCREAMING_SNAKE_CASE     						= torch.mean(torch.abs(lowercase			)			)

				assert abs(result_sum.item() - 2_02.02_96			) < 1e-2
				assert abs(result_mean.item() - 0.26_31			) < 1e-3







	def  snake_case__     (     self      :Optional[int]			)		->      List[Any]:







				"""simple docstring"""






				SCREAMING_SNAKE_CASE     						= self.scheduler_classes[0]
				SCREAMING_SNAKE_CASE     						= self.get_scheduler_config()
				SCREAMING_SNAKE_CASE     						= scheduler_class(**lowercase			)

				SCREAMING_SNAKE_CASE     						= [1_0_0, 8_7, 5_0, 1, 0]

				scheduler.set_timesteps(timesteps=lowercase			)

				SCREAMING_SNAKE_CASE     						= scheduler.timesteps

				for i, timestep in enumerate(lowercase			):
							if i == len(lowercase			) - 1:
										SCREAMING_SNAKE_CASE     						= -1
							else:
										SCREAMING_SNAKE_CASE     						= timesteps[i + 1]

							SCREAMING_SNAKE_CASE     						= scheduler.previous_timestep(lowercase			)
							SCREAMING_SNAKE_CASE     						= prev_t.item()

							self.assertEqual(lowercase   ,     lowercase			)







	def  snake_case__     (     self      :Tuple			)		->      List[str]:







				"""simple docstring"""






				SCREAMING_SNAKE_CASE     						= self.scheduler_classes[0]
				SCREAMING_SNAKE_CASE     						= self.get_scheduler_config()
				SCREAMING_SNAKE_CASE     						= scheduler_class(**lowercase			)

				SCREAMING_SNAKE_CASE     						= [1_0_0, 8_7, 5_0, 5_1, 0]

				with self.assertRaises(lowercase   ,     msg='''`custom_timesteps` must be in descending order.'''			):
							scheduler.set_timesteps(timesteps=lowercase			)







	def  snake_case__     (     self      :Optional[int]			)		->      int:







				"""simple docstring"""






				SCREAMING_SNAKE_CASE     						= self.scheduler_classes[0]
				SCREAMING_SNAKE_CASE     						= self.get_scheduler_config()
				SCREAMING_SNAKE_CASE     						= scheduler_class(**lowercase			)

				SCREAMING_SNAKE_CASE     						= [1_0_0, 8_7, 5_0, 1, 0]
				SCREAMING_SNAKE_CASE     						= len(lowercase			)

				with self.assertRaises(lowercase   ,     msg='''Can only pass one of `num_inference_steps` or `custom_timesteps`.'''			):
							scheduler.set_timesteps(num_inference_steps=lowercase   ,     timesteps=lowercase			)







	def  snake_case__     (     self      :str			)		->      Dict:







				"""simple docstring"""






				SCREAMING_SNAKE_CASE     						= self.scheduler_classes[0]
				SCREAMING_SNAKE_CASE     						= self.get_scheduler_config()
				SCREAMING_SNAKE_CASE     						= scheduler_class(**lowercase			)

				SCREAMING_SNAKE_CASE     						= [scheduler.config.num_train_timesteps]

				with self.assertRaises(
				    lowercase   ,     msg='''`timesteps` must start before `self.config.train_timesteps`: {scheduler.config.num_train_timesteps}}'''   ,     ):
							scheduler.set_timesteps(timesteps=lowercase			)