
"""simple docstring"""






from math import factorial

lowerCamelCase__ :       dict[str, int]						     =			{str(digit): factorial(digit) for digit in range(10)}





def __A						(   a_ :							List[Any]     )->							int:




		'''simple docstring'''






		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						(   a_ :							Tuple = 60		,		a_ :							List[str] = 1_00_00_00     )->							int:




		'''simple docstring'''






		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
		SCREAMING_SNAKE_CASE       :     str				= 0
		# the cached sizes of the previous chains
		SCREAMING_SNAKE_CASE       :     dict[int, int]				= {}

		for start_chain_element in range(1		,		__lowerCAmelCase     ):
				# The temporary set will contain the elements of the chain
				SCREAMING_SNAKE_CASE       :     Optional[Any]				= set()
				SCREAMING_SNAKE_CASE       :     List[str]				= 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       :     str				= 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
						SCREAMING_SNAKE_CASE       :     Union[str, Any]				= digit_factorial_sum(__lowerCAmelCase     )

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

				SCREAMING_SNAKE_CASE       :     str				= 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()}''')







"""simple docstring"""






from collections import OrderedDict
from typing import Any, Mapping, Optional

from ... import PreTrainedTokenizer
from ...configuration_utils import PretrainedConfig
from ...file_utils import TensorType, is_torch_available
from ...onnx import OnnxConfig, OnnxConfigWithPast, OnnxSeqaSeqConfigWithPast
from ...onnx.utils import compute_effective_axis_dimension
from ...utils import logging


lowerCamelCase__ :       Tuple						     =			logging.get_logger(__name__)

lowerCamelCase__ :       str						     =			{
    "facebook/blenderbot_small-90M": "https://huggingface.co/facebook/blenderbot_small-90M/resolve/main/config.json",
    # See all BlenderbotSmall models at https://huggingface.co/models?filter=blenderbot_small
}




class 				lowercase__(				_UpperCAmelCase   ):
	'''simple docstring'''

	UpperCamelCase				=  """blenderbot-small"""
	UpperCamelCase				=  ["""past_key_values"""]
	UpperCamelCase				=  {"""num_attention_heads""": """encoder_attention_heads""", """hidden_size""": """d_model"""}





	def __init__(						self    :Any		, lowerCamelCase_    :Dict=5_02_65		, lowerCamelCase_    :str=5_12		, lowerCamelCase_    :Tuple=8		, lowerCamelCase_    :int=20_48		, lowerCamelCase_    :str=16		, lowerCamelCase_    :Optional[int]=8		, lowerCamelCase_    :str=20_48		, lowerCamelCase_    :Optional[Any]=16		, lowerCamelCase_    :Union[str, Any]=0.0		, lowerCamelCase_    :List[str]=0.0		, lowerCamelCase_    :Tuple=True		, lowerCamelCase_    :Tuple=True		, lowerCamelCase_    :int="gelu"		, lowerCamelCase_    :Tuple=5_12		, lowerCamelCase_    :Optional[int]=0.1		, lowerCamelCase_    :int=0.0		, lowerCamelCase_    :Tuple=0.0		, lowerCamelCase_    :Optional[int]=0.0_2		, lowerCamelCase_    :Union[str, Any]=1		, lowerCamelCase_    :Dict=False		, lowerCamelCase_    :Optional[int]=0		, lowerCamelCase_    :List[Any]=1		, lowerCamelCase_    :Any=2		, lowerCamelCase_    :Optional[Any]=2		, **lowerCamelCase_    :Dict		, )							->			Any:







			'''simple docstring'''




			SCREAMING_SNAKE_CASE       :     int				= vocab_size
			SCREAMING_SNAKE_CASE       :     List[str]				= max_position_embeddings
			SCREAMING_SNAKE_CASE       :     Optional[Any]				= d_model
			SCREAMING_SNAKE_CASE       :     Dict				= encoder_ffn_dim
			SCREAMING_SNAKE_CASE       :     Tuple				= encoder_layers
			SCREAMING_SNAKE_CASE       :     Dict				= encoder_attention_heads
			SCREAMING_SNAKE_CASE       :     Any				= decoder_ffn_dim
			SCREAMING_SNAKE_CASE       :     str				= decoder_layers
			SCREAMING_SNAKE_CASE       :     str				= decoder_attention_heads
			SCREAMING_SNAKE_CASE       :     List[Any]				= dropout
			SCREAMING_SNAKE_CASE       :     Optional[Any]				= attention_dropout
			SCREAMING_SNAKE_CASE       :     Any				= activation_dropout
			SCREAMING_SNAKE_CASE       :     List[str]				= activation_function
			SCREAMING_SNAKE_CASE       :     Optional[int]				= init_std
			SCREAMING_SNAKE_CASE       :     List[Any]				= encoder_layerdrop
			SCREAMING_SNAKE_CASE       :     Union[str, Any]				= decoder_layerdrop
			SCREAMING_SNAKE_CASE       :     List[Any]				= use_cache
			SCREAMING_SNAKE_CASE       :     Union[str, Any]				= encoder_layers
			SCREAMING_SNAKE_CASE       :     List[Any]				= scale_embedding  # scale factor will be sqrt(d_model) if True

			super().__init__(
			    pad_token_id=lowerCamelCase_		, bos_token_id=lowerCamelCase_		, eos_token_id=lowerCamelCase_		, is_encoder_decoder=lowerCamelCase_		, decoder_start_token_id=lowerCamelCase_		, forced_eos_token_id=lowerCamelCase_		, **lowerCamelCase_		, )





class 				lowercase__(				_UpperCAmelCase   ):
	'''simple docstring'''

	@property
	def   __lowerCAmelCase (						self    :Any					)							->			Mapping[str, Mapping[int, str]]:







			'''simple docstring'''




			if self.task in ["default", "seq2seq-lm"]:
					SCREAMING_SNAKE_CASE       :     Tuple				= OrderedDict(
					    [
					        ('''input_ids''', {0: '''batch''', 1: '''encoder_sequence'''}),
					        ('''attention_mask''', {0: '''batch''', 1: '''encoder_sequence'''}),
					    ]					)

					if self.use_past:
							SCREAMING_SNAKE_CASE       :     Union[str, Any]				= {0: '''batch'''}
							SCREAMING_SNAKE_CASE       :     List[Any]				= {0: '''batch''', 1: '''past_decoder_sequence + sequence'''}
					else:
							SCREAMING_SNAKE_CASE       :     Optional[Any]				= {0: '''batch''', 1: '''decoder_sequence'''}
							SCREAMING_SNAKE_CASE       :     Union[str, Any]				= {0: '''batch''', 1: '''decoder_sequence'''}

					if self.use_past:
							self.fill_with_past_key_values_(lowerCamelCase_		, direction='''inputs'''					)
			elif self.task == "causal-lm":
					# TODO: figure this case out.
					SCREAMING_SNAKE_CASE       :     Tuple				= OrderedDict(
					    [
					        ('''input_ids''', {0: '''batch''', 1: '''encoder_sequence'''}),
					        ('''attention_mask''', {0: '''batch''', 1: '''encoder_sequence'''}),
					    ]					)
					if self.use_past:
							SCREAMING_SNAKE_CASE,					SCREAMING_SNAKE_CASE       :     List[Any]				= self.num_layers
							for i in range(lowerCamelCase_					):
									SCREAMING_SNAKE_CASE       :     int				= {0: '''batch''', 2: '''past_sequence + sequence'''}
									SCREAMING_SNAKE_CASE       :     List[str]				= {0: '''batch''', 2: '''past_sequence + sequence'''}
			else:
					SCREAMING_SNAKE_CASE       :     Any				= OrderedDict(
					    [
					        ('''input_ids''', {0: '''batch''', 1: '''encoder_sequence'''}),
					        ('''attention_mask''', {0: '''batch''', 1: '''encoder_sequence'''}),
					        ('''decoder_input_ids''', {0: '''batch''', 1: '''decoder_sequence'''}),
					        ('''decoder_attention_mask''', {0: '''batch''', 1: '''decoder_sequence'''}),
					    ]					)

			return common_inputs





	@property
	def   __lowerCAmelCase (						self    :List[str]					)							->			Mapping[str, Mapping[int, str]]:







			'''simple docstring'''




			if self.task in ["default", "seq2seq-lm"]:
					SCREAMING_SNAKE_CASE       :     Any				= super().outputs
			else:
					SCREAMING_SNAKE_CASE       :     Tuple				= super(lowerCamelCase_		, self					).outputs
					if self.use_past:
							SCREAMING_SNAKE_CASE,					SCREAMING_SNAKE_CASE       :     Union[str, Any]				= self.num_layers
							for i in range(lowerCamelCase_					):
									SCREAMING_SNAKE_CASE       :     Union[str, Any]				= {0: '''batch''', 2: '''past_sequence + sequence'''}
									SCREAMING_SNAKE_CASE       :     str				= {0: '''batch''', 2: '''past_sequence + sequence'''}
			return common_outputs





	def   __lowerCAmelCase (						self    :int		, lowerCamelCase_    :PreTrainedTokenizer		, lowerCamelCase_    :int = -1		, lowerCamelCase_    :int = -1		, lowerCamelCase_    :bool = False		, lowerCamelCase_    :Optional[TensorType] = None		, )							->			Mapping[str, Any]:







			'''simple docstring'''




			SCREAMING_SNAKE_CASE       :     Dict				= self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
			    lowerCamelCase_		, lowerCamelCase_		, lowerCamelCase_		, lowerCamelCase_		, lowerCamelCase_					)

			# Generate decoder inputs
			SCREAMING_SNAKE_CASE       :     Optional[int]				= seq_length if not self.use_past else 1
			SCREAMING_SNAKE_CASE       :     Optional[int]				= self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
			    lowerCamelCase_		, lowerCamelCase_		, lowerCamelCase_		, lowerCamelCase_		, lowerCamelCase_					)
			SCREAMING_SNAKE_CASE       :     List[Any]				= {f"decoder_{name}": tensor for name, tensor in decoder_inputs.items()}
			SCREAMING_SNAKE_CASE       :     str				= dict(**lowerCamelCase_		, **lowerCamelCase_					)

			if self.use_past:
					if not is_torch_available():
							raise ValueError('''Cannot generate dummy past_keys inputs without PyTorch installed.'''					)
					else:
							import torch
					SCREAMING_SNAKE_CASE,					SCREAMING_SNAKE_CASE       :     Any				= common_inputs['''input_ids'''].shape
					SCREAMING_SNAKE_CASE       :     str				= common_inputs['''decoder_input_ids'''].shape[1]
					SCREAMING_SNAKE_CASE,					SCREAMING_SNAKE_CASE       :     Any				= self.num_attention_heads
					SCREAMING_SNAKE_CASE       :     str				= (
					    batch,
					    num_encoder_attention_heads,
					    encoder_seq_length,
					    self._config.hidden_size // num_encoder_attention_heads,
					)
					SCREAMING_SNAKE_CASE       :     Optional[Any]				= decoder_seq_length + 3
					SCREAMING_SNAKE_CASE       :     int				= (
					    batch,
					    num_decoder_attention_heads,
					    decoder_past_length,
					    self._config.hidden_size // num_decoder_attention_heads,
					)

					SCREAMING_SNAKE_CASE       :     List[Any]				= torch.cat(
					    [common_inputs['''decoder_attention_mask'''], torch.ones(lowerCamelCase_		, lowerCamelCase_					)]		, dim=1					)

					SCREAMING_SNAKE_CASE       :     Optional[int]				= []
					# If the number of encoder and decoder layers are present in the model configuration, both are considered
					SCREAMING_SNAKE_CASE,					SCREAMING_SNAKE_CASE       :     Optional[int]				= self.num_layers
					SCREAMING_SNAKE_CASE       :     int				= min(lowerCamelCase_		, lowerCamelCase_					)
					SCREAMING_SNAKE_CASE       :     Optional[int]				= max(lowerCamelCase_		, lowerCamelCase_					) - min_num_layers
					SCREAMING_SNAKE_CASE       :     Tuple				= '''encoder''' if num_encoder_layers > num_decoder_layers else '''decoder'''

					for _ in range(lowerCamelCase_					):
							common_inputs["past_key_values"].append(
							    (
							        torch.zeros(lowerCamelCase_					),
							        torch.zeros(lowerCamelCase_					),
							        torch.zeros(lowerCamelCase_					),
							        torch.zeros(lowerCamelCase_					),
							    )					)
					# TODO: test this.
					SCREAMING_SNAKE_CASE       :     int				= encoder_shape if remaining_side_name == '''encoder''' else decoder_shape
					for _ in range(lowerCamelCase_		, lowerCamelCase_					):
							common_inputs["past_key_values"].append((torch.zeros(lowerCamelCase_					), torch.zeros(lowerCamelCase_					))					)
			return common_inputs





	def   __lowerCAmelCase (						self    :Any		, lowerCamelCase_    :PreTrainedTokenizer		, lowerCamelCase_    :int = -1		, lowerCamelCase_    :int = -1		, lowerCamelCase_    :bool = False		, lowerCamelCase_    :Optional[TensorType] = None		, )							->			Mapping[str, Any]:







			'''simple docstring'''




			SCREAMING_SNAKE_CASE       :     Any				= self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
			    lowerCamelCase_		, lowerCamelCase_		, lowerCamelCase_		, lowerCamelCase_		, lowerCamelCase_					)

			if self.use_past:
					if not is_torch_available():
							raise ValueError('''Cannot generate dummy past_keys inputs without PyTorch installed.'''					)
					else:
							import torch
					SCREAMING_SNAKE_CASE,					SCREAMING_SNAKE_CASE       :     Tuple				= common_inputs['''input_ids'''].shape
					# Not using the same length for past_key_values
					SCREAMING_SNAKE_CASE       :     List[str]				= seqlen + 2
					SCREAMING_SNAKE_CASE,					SCREAMING_SNAKE_CASE       :     Dict				= self.num_layers
					SCREAMING_SNAKE_CASE,					SCREAMING_SNAKE_CASE       :     List[Any]				= self.num_attention_heads
					SCREAMING_SNAKE_CASE       :     Union[str, Any]				= (
					    batch,
					    num_encoder_attention_heads,
					    past_key_values_length,
					    self._config.hidden_size // num_encoder_attention_heads,
					)

					SCREAMING_SNAKE_CASE       :     Tuple				= common_inputs['''attention_mask'''].dtype
					SCREAMING_SNAKE_CASE       :     Any				= torch.cat(
					    [common_inputs['''attention_mask'''], torch.ones(lowerCamelCase_		, lowerCamelCase_		, dtype=lowerCamelCase_					)]		, dim=1					)
					SCREAMING_SNAKE_CASE       :     Optional[int]				= [
					    (torch.zeros(lowerCamelCase_					), torch.zeros(lowerCamelCase_					)) for _ in range(lowerCamelCase_					)
					]
			return common_inputs





	def   __lowerCAmelCase (						self    :Union[str, Any]		, lowerCamelCase_    :PreTrainedTokenizer		, lowerCamelCase_    :int = -1		, lowerCamelCase_    :int = -1		, lowerCamelCase_    :bool = False		, lowerCamelCase_    :Optional[TensorType] = None		, )							->			Mapping[str, Any]:







			'''simple docstring'''




			SCREAMING_SNAKE_CASE       :     List[str]				= compute_effective_axis_dimension(
			    lowerCamelCase_		, fixed_dimension=OnnxConfig.default_fixed_batch		, num_token_to_add=0					)

			# If dynamic axis (-1) we forward with a fixed dimension of 8 tokens to avoid optimizations made by ONNX
			SCREAMING_SNAKE_CASE       :     int				= tokenizer.num_special_tokens_to_add(lowerCamelCase_					)
			SCREAMING_SNAKE_CASE       :     int				= compute_effective_axis_dimension(
			    lowerCamelCase_		, fixed_dimension=OnnxConfig.default_fixed_sequence		, num_token_to_add=lowerCamelCase_					)

			# Generate dummy inputs according to compute batch and sequence
			SCREAMING_SNAKE_CASE       :     Tuple				= [''' '''.join([tokenizer.unk_token]					) * seq_length] * batch_size
			SCREAMING_SNAKE_CASE       :     Any				= dict(tokenizer(lowerCamelCase_		, return_tensors=lowerCamelCase_					)					)
			return common_inputs





	def   __lowerCAmelCase (						self    :List[Any]		, lowerCamelCase_    :PreTrainedTokenizer		, lowerCamelCase_    :int = -1		, lowerCamelCase_    :int = -1		, lowerCamelCase_    :bool = False		, lowerCamelCase_    :Optional[TensorType] = None		, )							->			Mapping[str, Any]:







			'''simple docstring'''




			if self.task in ["default", "seq2seq-lm"]:
					SCREAMING_SNAKE_CASE       :     Dict				= self._generate_dummy_inputs_for_default_and_seqaseq_lm(
					    lowerCamelCase_		, batch_size=lowerCamelCase_		, seq_length=lowerCamelCase_		, is_pair=lowerCamelCase_		, framework=lowerCamelCase_					)

			elif self.task == "causal-lm":
					SCREAMING_SNAKE_CASE       :     Union[str, Any]				= self._generate_dummy_inputs_for_causal_lm(
					    lowerCamelCase_		, batch_size=lowerCamelCase_		, seq_length=lowerCamelCase_		, is_pair=lowerCamelCase_		, framework=lowerCamelCase_					)
			else:
					SCREAMING_SNAKE_CASE       :     List[Any]				= self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
					    lowerCamelCase_		, batch_size=lowerCamelCase_		, seq_length=lowerCamelCase_		, is_pair=lowerCamelCase_		, framework=lowerCamelCase_					)

			return common_inputs







	def   __lowerCAmelCase (						self    :Dict		, lowerCamelCase_    :int		, lowerCamelCase_    :List[str]		, lowerCamelCase_    :List[str]		, lowerCamelCase_    :Dict					)							->			List[Any]:







			'''simple docstring'''




			if self.task in ["default", "seq2seq-lm"]:
					SCREAMING_SNAKE_CASE       :     Optional[Any]				= super()._flatten_past_key_values_(lowerCamelCase_		, lowerCamelCase_		, lowerCamelCase_		, lowerCamelCase_					)
			else:
					SCREAMING_SNAKE_CASE       :     Tuple				= super(lowerCamelCase_		, self					)._flatten_past_key_values_(
					    lowerCamelCase_		, lowerCamelCase_		, lowerCamelCase_		, lowerCamelCase_					)





