





from __future__ import annotations


def 					__SCREAMING_SNAKE_CASE  (							__lowercase:		int):



  '''simple docstring'''






  __lowerCAmelCase			=				[0] * max_one

  for i in range(0     ,							__lowercase):
    __lowerCAmelCase			=				i

  for i in range(2     ,							__lowercase):
    if totients[i] == i:
      for j in range(__lowercase     ,							__lowercase     ,							__lowercase):
        totients[j] -= totients[j] // i

  return totients


def 					__SCREAMING_SNAKE_CASE  (							__lowercase:		int     ,							__lowercase:		int):



  '''simple docstring'''






  return sorted(str(__lowercase)) == sorted(str(__lowercase))


def 					__SCREAMING_SNAKE_CASE  (							__lowercase:		int = 10_00_00_00):



  '''simple docstring'''






  __lowerCAmelCase			=				1  # i
  __lowerCAmelCase			=				0  # φ(i)
  __lowerCAmelCase			=				get_totients(max_n + 1)

  for i in range(2     ,							max_n + 1):
    __lowerCAmelCase			=				totients[i]

    if i * min_denominator < min_numerator * t and has_same_digits(__lowercase     ,							__lowercase):
      __lowerCAmelCase			=				i
      __lowerCAmelCase			=				t

  return min_numerator


if __name__ == "__main__":
      print(f"""{solution() = }""")







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


__lowercase													=			logging.get_logger(__name__)

__lowercase													=			{
    """facebook/blenderbot-3B""": """https://huggingface.co/facebook/blenderbot-3B/resolve/main/config.json""",
    # See all Blenderbot models at https://huggingface.co/models?filter=blenderbot
}

class   __snake_case				(			_a   ):






    '''simple docstring'''
    _lowerCAmelCase     =	"""blenderbot"""
    _lowerCAmelCase     =	["""past_key_values"""]
    _lowerCAmelCase     =	{"""num_attention_heads""": """encoder_attention_heads""", """hidden_size""": """d_model"""}





    def __init__(   self						:		Any			,						snake_case						:		Union[str, Any]=8_008			,						snake_case						:		List[str]=128			,						snake_case						:		Tuple=2			,						snake_case						:		int=10_240			,						snake_case						:		Optional[int]=32			,						snake_case						:		Dict=24			,						snake_case						:		List[Any]=10_240			,						snake_case						:		Optional[int]=32			,						snake_case						:		List[str]=0.0			,						snake_case						:		Optional[int]=0.0			,						snake_case						:		Optional[Any]=True			,						snake_case						:		int=True			,						snake_case						:		List[str]="gelu"			,						snake_case						:		Any=2_560			,						snake_case						:		Optional[Any]=0.1			,						snake_case						:		Union[str, Any]=0.0			,						snake_case						:		List[Any]=0.0			,						snake_case						:		Dict=0.02			,						snake_case						:		int=1			,						snake_case						:		Dict=False			,						snake_case						:		List[str]=0			,						snake_case						:		Optional[Any]=1			,						snake_case						:		List[Any]=2			,						snake_case						:		List[str]=3			,						snake_case						:		List[str]=2			,						**snake_case						:		int			,						):

      """simple docstring"""





      __lowerCAmelCase			=				vocab_size
      __lowerCAmelCase			=				max_position_embeddings
      __lowerCAmelCase			=				d_model
      __lowerCAmelCase			=				encoder_ffn_dim
      __lowerCAmelCase			=				encoder_layers
      __lowerCAmelCase			=				encoder_attention_heads
      __lowerCAmelCase			=				decoder_ffn_dim
      __lowerCAmelCase			=				decoder_layers
      __lowerCAmelCase			=				decoder_attention_heads
      __lowerCAmelCase			=				dropout
      __lowerCAmelCase			=				attention_dropout
      __lowerCAmelCase			=				activation_dropout
      __lowerCAmelCase			=				activation_function
      __lowerCAmelCase			=				init_std
      __lowerCAmelCase			=				encoder_layerdrop
      __lowerCAmelCase			=				decoder_layerdrop
      __lowerCAmelCase			=				use_cache
      __lowerCAmelCase			=				encoder_layers
      __lowerCAmelCase			=				scale_embedding  # scale factor will be sqrt(d_model) if True

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


class   __snake_case				(			_a   ):






    '''simple docstring'''





    @property
    def 	A		(   self						:		int							):

      """simple docstring"""





      if self.task in ["default", "seq2seq-lm"]:
        __lowerCAmelCase			=				OrderedDict(
            [
                ('''input_ids''', {0: '''batch''', 1: '''encoder_sequence'''}),
                ('''attention_mask''', {0: '''batch''', 1: '''encoder_sequence'''}),
            ]							)
        if self.use_past:
          __lowerCAmelCase			=				{0: '''batch'''}
          __lowerCAmelCase			=				{0: '''batch''', 1: '''past_decoder_sequence + sequence'''}
        else:
          __lowerCAmelCase			=				{0: '''batch''', 1: '''decoder_sequence'''}
          __lowerCAmelCase			=				{0: '''batch''', 1: '''decoder_sequence'''}
        if self.use_past:
          self.fill_with_past_key_values_(snake_case			,						direction='''inputs'''							)
      elif self.task == "causal-lm":
        __lowerCAmelCase			=				OrderedDict(
            [
                ('''input_ids''', {0: '''batch''', 1: '''encoder_sequence'''}),
                ('''attention_mask''', {0: '''batch''', 1: '''encoder_sequence'''}),
            ]							)
        if self.use_past:
          __lowerCAmelCase	,						__lowerCAmelCase			=				self.num_layers
          for i in range(snake_case							):
            __lowerCAmelCase			=				{0: '''batch''', 2: '''past_sequence + sequence'''}
            __lowerCAmelCase			=				{0: '''batch''', 2: '''past_sequence + sequence'''}
      else:
        __lowerCAmelCase			=				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
    # Copied from transformers.models.bart.configuration_bart.BartOnnxConfig.outputs
    def 	A		(   self						:		Optional[Any]							):

      """simple docstring"""





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





    def 	A		(   self						:		int			,						snake_case						:		PreTrainedTokenizer			,						snake_case						:		int = -1			,						snake_case						:		int = -1			,						snake_case						:		bool = False			,						snake_case						:		Optional[TensorType] = None			,						):

      """simple docstring"""





      __lowerCAmelCase			=				self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
          snake_case			,						snake_case			,						snake_case			,						snake_case			,						snake_case							)
      # Generate decoder inputs
      __lowerCAmelCase			=				seq_length if not self.use_past else 1
      __lowerCAmelCase			=				self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
          snake_case			,						snake_case			,						snake_case			,						snake_case			,						snake_case							)
      __lowerCAmelCase			=				{f'''decoder_{name}''': tensor for name, tensor in decoder_inputs.items()}
      __lowerCAmelCase			=				dict(**snake_case			,						**snake_case							)

      if self.use_past:
        if not is_torch_available():
          raise ValueError('''Cannot generate dummy past_keys inputs without PyTorch installed.'''							)
        else:
          import torch
        __lowerCAmelCase	,						__lowerCAmelCase			=				common_inputs['''input_ids'''].shape
        __lowerCAmelCase			=				common_inputs['''decoder_input_ids'''].shape[1]
        __lowerCAmelCase	,						__lowerCAmelCase			=				self.num_attention_heads
        __lowerCAmelCase			=				(
            batch,
            num_encoder_attention_heads,
            encoder_seq_length,
            self._config.hidden_size // num_encoder_attention_heads,
        )
        __lowerCAmelCase			=				decoder_seq_length
        __lowerCAmelCase			=				(
            batch,
            num_decoder_attention_heads,
            decoder_past_length,
            self._config.hidden_size // num_decoder_attention_heads,
        )
        __lowerCAmelCase			=				torch.cat(
            [common_inputs['''decoder_attention_mask'''], torch.ones(snake_case			,						snake_case							)]			,						dim=1							)
        __lowerCAmelCase			=				[]
        __lowerCAmelCase	,						__lowerCAmelCase			=				self.num_layers

        for _ in range(snake_case							):
          common_inputs["past_key_values"].append(
              (
                  torch.zeros(snake_case							),
                  torch.zeros(snake_case							),
                  torch.zeros(snake_case							),
                  torch.zeros(snake_case							),
              )							)
      return common_inputs





    def 	A		(   self						:		str			,						snake_case						:		PreTrainedTokenizer			,						snake_case						:		int = -1			,						snake_case						:		int = -1			,						snake_case						:		bool = False			,						snake_case						:		Optional[TensorType] = None			,						):

      """simple docstring"""





      __lowerCAmelCase			=				self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
          snake_case			,						snake_case			,						snake_case			,						snake_case			,						snake_case							)

      if self.use_past:
        if not is_torch_available():
          raise ValueError('''Cannot generate dummy past_keys inputs without PyTorch installed.'''							)
        else:
          import torch
        __lowerCAmelCase	,						__lowerCAmelCase			=				common_inputs['''input_ids'''].shape
        __lowerCAmelCase			=				seqlen
        __lowerCAmelCase	,						__lowerCAmelCase			=				self.num_layers
        __lowerCAmelCase	,						__lowerCAmelCase			=				self.num_attention_heads
        __lowerCAmelCase			=				(
            batch,
            num_encoder_attention_heads,
            past_key_values_length,
            self._config.hidden_size // num_encoder_attention_heads,
        )
        __lowerCAmelCase			=				common_inputs['''attention_mask'''].dtype
        __lowerCAmelCase			=				torch.cat(
            [common_inputs['''attention_mask'''], torch.ones(snake_case			,						snake_case			,						dtype=snake_case							)]			,						dim=1							)
        __lowerCAmelCase			=				[
            (torch.zeros(snake_case							), torch.zeros(snake_case							)) for _ in range(snake_case							)
        ]
      return common_inputs





    def 	A		(   self						:		Optional[int]			,						snake_case						:		PreTrainedTokenizer			,						snake_case						:		int = -1			,						snake_case						:		int = -1			,						snake_case						:		bool = False			,						snake_case						:		Optional[TensorType] = None			,						):

      """simple docstring"""





      __lowerCAmelCase			=				compute_effective_axis_dimension(
          snake_case			,						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
      __lowerCAmelCase			=				tokenizer.num_special_tokens_to_add(snake_case							)
      __lowerCAmelCase			=				compute_effective_axis_dimension(
          snake_case			,						fixed_dimension=OnnxConfig.default_fixed_sequence			,						num_token_to_add=snake_case							)

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





    def 	A		(   self						:		str			,						snake_case						:		PreTrainedTokenizer			,						snake_case						:		int = -1			,						snake_case						:		int = -1			,						snake_case						:		bool = False			,						snake_case						:		Optional[TensorType] = None			,						):

      """simple docstring"""





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

      elif self.task == "causal-lm":
        __lowerCAmelCase			=				self._generate_dummy_inputs_for_causal_lm(
            snake_case			,						batch_size=snake_case			,						seq_length=snake_case			,						is_pair=snake_case			,						framework=snake_case							)
      else:
        __lowerCAmelCase			=				self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
            snake_case			,						batch_size=snake_case			,						seq_length=snake_case			,						is_pair=snake_case			,						framework=snake_case							)

      return common_inputs





    def 	A		(   self						:		Optional[Any]			,						snake_case						:		int			,						snake_case						:		str			,						snake_case						:		str			,						snake_case						:		List[str]							):

      """simple docstring"""





      if self.task in ["default", "seq2seq-lm"]:
        __lowerCAmelCase			=				super()._flatten_past_key_values_(snake_case			,						snake_case			,						snake_case			,						snake_case							)
      else:
        __lowerCAmelCase			=				super(snake_case			,						self							)._flatten_past_key_values_(
            snake_case			,						snake_case			,						snake_case			,						snake_case							)





    def 	A		(   self						:		List[Any]			,						snake_case						:		Mapping[str, Mapping[int, str]]			,						snake_case						:		str							):

      """simple docstring"""





      if direction not in ["inputs", "outputs"]:
        raise ValueError(f'''direction must either be "inputs" or "outputs", but {direction} was given'''							)

      __lowerCAmelCase			=				'''past_key_values''' if direction == '''inputs''' else '''present'''
      __lowerCAmelCase	,						__lowerCAmelCase			=				self.num_layers

      __lowerCAmelCase			=				'''past_encoder_sequence'''
      __lowerCAmelCase			=				'''past_decoder_sequence''' if direction == '''inputs''' else '''past_decoder_sequence + sequence'''

      for i in range(snake_case							):
        __lowerCAmelCase			=				{0: '''batch''', 2: decoder_sequence}
        __lowerCAmelCase			=				{0: '''batch''', 2: decoder_sequence}
        __lowerCAmelCase			=				{0: '''batch''', 2: encoder_sequence}
        __lowerCAmelCase			=				{0: '''batch''', 2: encoder_sequence}
