






"""simple docstring"""
from collections import OrderedDict
from typing import Any, Mapping, Optional

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


A_     :					Optional[Any]							=     logging.get_logger(__name__)

A_     :					str							=     {
    "google/bigbird-pegasus-large-arxiv": (
        "https://huggingface.co/google/bigbird-pegasus-large-arxiv/resolve/main/config.json"
    ),
    "google/bigbird-pegasus-large-pubmed": (
        "https://huggingface.co/google/bigbird-pegasus-large-pubmed/resolve/main/config.json"
    ),
    "google/bigbird-pegasus-large-bigpatent": (
        "https://huggingface.co/google/bigbird-pegasus-large-bigpatent/resolve/main/config.json"
    ),
    # See all BigBirdPegasus models at https://huggingface.co/models?filter=bigbird_pegasus
}



class 						a_ (      snake_case_					):







      '''simple docstring'''

      lowerCamelCase__			:							Tuple					=      'bigbird_pegasus'
      lowerCamelCase__			:							List[str]					=      ['past_key_values']
      lowerCamelCase__			:							Union[str, Any]					=      {
          'num_attention_heads': 'encoder_attention_heads',
          'hidden_size': 'd_model',
          'attention_probs_dropout_prob': 'attention_dropout',
      }




      def __init__(self,	lowerCamelCase_=9_6_1_0_3,	lowerCamelCase_=4_0_9_6,	lowerCamelCase_=1_6,	lowerCamelCase_=4_0_9_6,	lowerCamelCase_=1_6,	lowerCamelCase_=1_6,	lowerCamelCase_=4_0_9_6,	lowerCamelCase_=1_6,	lowerCamelCase_=0.0,	lowerCamelCase_=0.0,	lowerCamelCase_=True,	lowerCamelCase_=True,	lowerCamelCase_="gelu_new",	lowerCamelCase_=1_0_2_4,	lowerCamelCase_=0.1,	lowerCamelCase_=0.0,	lowerCamelCase_=0.0,	lowerCamelCase_=0.02,	lowerCamelCase_=2,	lowerCamelCase_=0.0,	lowerCamelCase_=True,	lowerCamelCase_=0,	lowerCamelCase_=2,	lowerCamelCase_=1,	lowerCamelCase_="block_sparse",	lowerCamelCase_=6_4,	lowerCamelCase_=3,	lowerCamelCase_=False,	**lowerCamelCase_,	):

       '''simple docstring'''



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

       # extra config
       lowerCamelCase__	:     Optional[Any]								=		attention_type
       lowerCamelCase__	:     Optional[Any]								=		block_size
       lowerCamelCase__	:     str								=		num_random_blocks
       lowerCamelCase__	:     Optional[Any]								=		use_bias

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



class 						a_ (      snake_case_					):







      '''simple docstring'''

      @property
      def      a__				(self   ):

       '''simple docstring'''



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

        if self.use_past:
         lowerCamelCase__	:     List[Any]								=		{0: 'batch'}
         lowerCamelCase__	:     Optional[int]								=		{0: 'batch', 1: 'past_decoder_sequence + sequence'}
        else:
         lowerCamelCase__	:     List[str]								=		{0: 'batch', 1: 'decoder_sequence'}
         lowerCamelCase__	:     List[str]								=		{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.
        lowerCamelCase__	:     Any								=		OrderedDict(
            [
                ('input_ids', {0: 'batch', 1: 'encoder_sequence'}),
                ('attention_mask', {0: 'batch', 1: 'encoder_sequence'}),
            ]   )
        if self.use_past:
         lowerCamelCase__							,	lowerCamelCase__	:     Union[str, Any]								=		self.num_layers
         for i in range(lowerCamelCase_   ):
          lowerCamelCase__	:     Dict								=		{0: 'batch', 2: 'past_sequence + sequence'}
          lowerCamelCase__	:     Tuple								=		{0: 'batch', 2: 'past_sequence + sequence'}
       else:
        lowerCamelCase__	:     str								=		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      a__				(self   ):

       '''simple docstring'''



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




      def      a__				(self,	lowerCamelCase_,	lowerCamelCase_ = -1,	lowerCamelCase_ = -1,	lowerCamelCase_ = False,	lowerCamelCase_ = None,	):

       '''simple docstring'''



       lowerCamelCase__	:     str								=		self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
           lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_   )

       # Generate decoder inputs
       lowerCamelCase__	:     str								=		seq_length if not self.use_past else 1
       lowerCamelCase__	:     Optional[int]								=		self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
           lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_   )
       lowerCamelCase__	:     Optional[int]								=		{f'''decoder_{name}''': tensor for name, tensor in decoder_inputs.items()}
       lowerCamelCase__	:     int								=		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
        lowerCamelCase__							,	lowerCamelCase__	:     Union[str, Any]								=		common_inputs['input_ids'].shape
        lowerCamelCase__	:     List[Any]								=		common_inputs['decoder_input_ids'].shape[1]
        lowerCamelCase__							,	lowerCamelCase__	:     List[Any]								=		self.num_attention_heads
        lowerCamelCase__	:     str								=		(
            batch,
            num_encoder_attention_heads,
            encoder_seq_length,
            self._config.hidden_size // num_encoder_attention_heads,
        )
        lowerCamelCase__	:     int								=		decoder_seq_length + 3
        lowerCamelCase__	:     List[Any]								=		(
            batch,
            num_decoder_attention_heads,
            decoder_past_length,
            self._config.hidden_size // num_decoder_attention_heads,
        )

        lowerCamelCase__	:     Optional[int]								=		torch.cat(
            [common_inputs['decoder_attention_mask'], torch.ones(lowerCamelCase_,	lowerCamelCase_   )],	dim=1   )

        lowerCamelCase__	:     Any								=		[]
        # If the number of encoder and decoder layers are present in the model configuration, both are considered
        lowerCamelCase__							,	lowerCamelCase__	:     Optional[int]								=		self.num_layers
        lowerCamelCase__	:     Optional[Any]								=		min(lowerCamelCase_,	lowerCamelCase_   )
        lowerCamelCase__	:     int								=		max(lowerCamelCase_,	lowerCamelCase_   ) - min_num_layers
        lowerCamelCase__	:     Any								=		'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.
        lowerCamelCase__	:     List[Any]								=		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      a__				(self,	lowerCamelCase_,	lowerCamelCase_ = -1,	lowerCamelCase_ = -1,	lowerCamelCase_ = False,	lowerCamelCase_ = None,	):

       '''simple docstring'''



       lowerCamelCase__	:     List[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
        lowerCamelCase__							,	lowerCamelCase__	:     List[str]								=		common_inputs['input_ids'].shape
        # Not using the same length for past_key_values
        lowerCamelCase__	:     Optional[Any]								=		seqlen + 2
        lowerCamelCase__							,	lowerCamelCase__	:     Union[str, Any]								=		self.num_layers
        lowerCamelCase__							,	lowerCamelCase__	:     str								=		self.num_attention_heads
        lowerCamelCase__	:     Union[str, Any]								=		(
            batch,
            num_encoder_attention_heads,
            past_key_values_length,
            self._config.hidden_size // num_encoder_attention_heads,
        )

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




      def      a__				(self,	lowerCamelCase_,	lowerCamelCase_ = -1,	lowerCamelCase_ = -1,	lowerCamelCase_ = False,	lowerCamelCase_ = None,	):

       '''simple docstring'''



       lowerCamelCase__	:     List[Any]								=		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
       lowerCamelCase__	:     Optional[int]								=		tokenizer.num_special_tokens_to_add(lowerCamelCase_   )
       lowerCamelCase__	:     List[str]								=		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
       lowerCamelCase__	:     Optional[int]								=		[' '.join([tokenizer.unk_token]   ) * seq_length] * batch_size
       lowerCamelCase__	:     Tuple								=		dict(tokenizer(lowerCamelCase_,	return_tensors=lowerCamelCase_   )   )
       return common_inputs




      def      a__				(self,	lowerCamelCase_,	lowerCamelCase_ = -1,	lowerCamelCase_ = -1,	lowerCamelCase_ = False,	lowerCamelCase_ = None,	):

       '''simple docstring'''



       if self.task in ["default", "seq2seq-lm"]:
        lowerCamelCase__	:     Tuple								=		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":
        lowerCamelCase__	:     Optional[Any]								=		self._generate_dummy_inputs_for_causal_lm(
            lowerCamelCase_,	batch_size=lowerCamelCase_,	seq_length=lowerCamelCase_,	is_pair=lowerCamelCase_,	framework=lowerCamelCase_   )
       else:
        lowerCamelCase__	:     Tuple								=		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      a__				(self,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_,	lowerCamelCase_   ):

       '''simple docstring'''



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









"""simple docstring"""
from itertools import combinations, product






def 			lowerCamelCase_    (		_lowerCamelCase     ,  _lowerCamelCase     ,  _lowerCamelCase     ,  _lowerCamelCase							):
 if xa == ya == 0 or xa == ya == 0:
  return False
 lowerCamelCase__	:     Tuple								=		xa * xa + ya * ya
 lowerCamelCase__	:     Union[str, Any]								=		xa * xa + ya * ya
 lowerCamelCase__	:     Optional[Any]								=		(xa - xa) * (xa - xa) + (ya - ya) * (ya - ya)
 return (
     a_square + b_square == c_square
     or a_square + c_square == b_square
     or b_square + c_square == a_square
 )






def 			lowerCamelCase_    (		_lowerCamelCase = 50							):
 return sum(
     1
     for pta, pta in combinations(product(range(limit + 1							)     ,  repeat=2							)     ,  2							)
     if is_right(*_lowerCamelCase     ,  *_lowerCamelCase							)							)


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

