
"""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


snake_case    =		logging.get_logger(__name__)

snake_case    =		{
    'facebook/mbart-large-cc25': 'https://huggingface.co/facebook/mbart-large-cc25/resolve/main/config.json',
    # See all MBART models at https://huggingface.co/models?filter=mbart
}




class      UpperCamelCase	(       __magic_name__      ):

				"""simple docstring"""



				UpperCAmelCase_				:      List[Any]						  =				"mbart"
				UpperCAmelCase_				:      Any						  =				["past_key_values"]
				UpperCAmelCase_				:      Optional[int]						  =				{"num_attention_heads": "encoder_attention_heads", "hidden_size": "d_model"}


				def __init__(				self		,	lowercase__=50265		,	lowercase__=1024		,	lowercase__=12		,	lowercase__=4096		,	lowercase__=16		,	lowercase__=12		,	lowercase__=4096		,	lowercase__=16		,	lowercase__=0.0		,	lowercase__=0.0		,	lowercase__=True		,	lowercase__=True		,	lowercase__="gelu"		,	lowercase__=1024		,	lowercase__=0.1		,	lowercase__=0.0		,	lowercase__=0.0		,	lowercase__=0.02		,	lowercase__=0.0		,	lowercase__=False		,	lowercase__=1		,	lowercase__=0		,	lowercase__=2		,	lowercase__=2		,	**lowercase__		,	)    ->    Tuple:
									"""simple docstring"""







									SCREAMING_SNAKE_CASE				=	vocab_size
									SCREAMING_SNAKE_CASE				=	max_position_embeddings
									SCREAMING_SNAKE_CASE				=	d_model
									SCREAMING_SNAKE_CASE				=	encoder_ffn_dim
									SCREAMING_SNAKE_CASE				=	encoder_layers
									SCREAMING_SNAKE_CASE				=	encoder_attention_heads
									SCREAMING_SNAKE_CASE				=	decoder_ffn_dim
									SCREAMING_SNAKE_CASE				=	decoder_layers
									SCREAMING_SNAKE_CASE				=	decoder_attention_heads
									SCREAMING_SNAKE_CASE				=	dropout
									SCREAMING_SNAKE_CASE				=	attention_dropout
									SCREAMING_SNAKE_CASE				=	activation_dropout
									SCREAMING_SNAKE_CASE				=	activation_function
									SCREAMING_SNAKE_CASE				=	init_std
									SCREAMING_SNAKE_CASE				=	encoder_layerdrop
									SCREAMING_SNAKE_CASE				=	decoder_layerdrop
									SCREAMING_SNAKE_CASE				=	classifier_dropout
									SCREAMING_SNAKE_CASE				=	use_cache
									SCREAMING_SNAKE_CASE				=	encoder_layers
									SCREAMING_SNAKE_CASE				=	scale_embedding  # scale factor will be sqrt(d_model) if True
									super().__init__(
									    pad_token_id=lowercase__		,	bos_token_id=lowercase__		,	eos_token_id=lowercase__		,	is_encoder_decoder=lowercase__		,	forced_eos_token_id=lowercase__		,	**lowercase__		,	)






class      UpperCamelCase	(       __magic_name__      ):

				"""simple docstring"""



				@property
				def 							A					(				self			)    ->    Mapping[str, Mapping[int, str]]:
									"""simple docstring"""







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

														if self.use_past:
																			SCREAMING_SNAKE_CASE				=	{0: 'batch'}
																			SCREAMING_SNAKE_CASE				=	{0: 'batch', 1: 'past_decoder_sequence + sequence'}
														else:
																			SCREAMING_SNAKE_CASE				=	{0: 'batch', 1: 'decoder_sequence'}
																			SCREAMING_SNAKE_CASE				=	{0: 'batch', 1: 'decoder_sequence'}

														if self.use_past:
																			self.fill_with_past_key_values_(lowercase__		,	direction='inputs'			)
									elif self.task == "causal-lm":
														# TODO: figure this case out.
														SCREAMING_SNAKE_CASE				=	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				=	self.num_layers
																			for i in range(lowercase__			):
																								SCREAMING_SNAKE_CASE				=	{0: 'batch', 2: 'past_sequence + sequence'}
																								SCREAMING_SNAKE_CASE				=	{0: 'batch', 2: 'past_sequence + sequence'}
									else:
														SCREAMING_SNAKE_CASE				=	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			)    ->    Mapping[str, Mapping[int, str]]:
									"""simple docstring"""







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


				def 							A					(				self		,	lowercase__		,	lowercase__ = -1		,	lowercase__ = -1		,	lowercase__ = False		,	lowercase__ = None		,	)    ->    Mapping[str, Any]:
									"""simple docstring"""







									SCREAMING_SNAKE_CASE				=	self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
									    lowercase__		,	lowercase__		,	lowercase__		,	lowercase__		,	lowercase__			)

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

									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				=	common_inputs['input_ids'].shape
														SCREAMING_SNAKE_CASE				=	common_inputs['decoder_input_ids'].shape[1]
														SCREAMING_SNAKE_CASE	,    SCREAMING_SNAKE_CASE				=	self.num_attention_heads
														SCREAMING_SNAKE_CASE				=	(
														    batch,
														    num_encoder_attention_heads,
														    encoder_seq_length,
														    self._config.hidden_size // num_encoder_attention_heads,
														)
														SCREAMING_SNAKE_CASE				=	decoder_seq_length + 3
														SCREAMING_SNAKE_CASE				=	(
														    batch,
														    num_decoder_attention_heads,
														    decoder_past_length,
														    self._config.hidden_size // num_decoder_attention_heads,
														)

														SCREAMING_SNAKE_CASE				=	torch.cat(
														    [common_inputs['decoder_attention_mask'], torch.ones(lowercase__		,	lowercase__			)]		,	dim=1			)

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

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


				def 							A					(				self		,	lowercase__		,	lowercase__ = -1		,	lowercase__ = -1		,	lowercase__ = False		,	lowercase__ = None		,	)    ->    Mapping[str, Any]:
									"""simple docstring"""







									SCREAMING_SNAKE_CASE				=	self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
									    lowercase__		,	lowercase__		,	lowercase__		,	lowercase__		,	lowercase__			)

									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				=	common_inputs['input_ids'].shape
														# Not using the same length for past_key_values
														SCREAMING_SNAKE_CASE				=	seqlen + 2
														SCREAMING_SNAKE_CASE	,    SCREAMING_SNAKE_CASE				=	self.num_layers
														SCREAMING_SNAKE_CASE	,    SCREAMING_SNAKE_CASE				=	self.num_attention_heads
														SCREAMING_SNAKE_CASE				=	(
														    batch,
														    num_encoder_attention_heads,
														    past_key_values_length,
														    self._config.hidden_size // num_encoder_attention_heads,
														)

														SCREAMING_SNAKE_CASE				=	common_inputs['attention_mask'].dtype
														SCREAMING_SNAKE_CASE				=	torch.cat(
														    [common_inputs['attention_mask'], torch.ones(lowercase__		,	lowercase__		,	dtype=lowercase__			)]		,	dim=1			)
														SCREAMING_SNAKE_CASE				=	[
														    (torch.zeros(lowercase__			), torch.zeros(lowercase__			)) for _ in range(lowercase__			)
														]
									return common_inputs


				def 							A					(				self		,	lowercase__		,	lowercase__ = -1		,	lowercase__ = -1		,	lowercase__ = False		,	lowercase__ = None		,	)    ->    Mapping[str, Any]:
									"""simple docstring"""







									SCREAMING_SNAKE_CASE				=	compute_effective_axis_dimension(
									    lowercase__		,	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				=	tokenizer.num_special_tokens_to_add(lowercase__			)
									SCREAMING_SNAKE_CASE				=	compute_effective_axis_dimension(
									    lowercase__		,	fixed_dimension=OnnxConfig.default_fixed_sequence		,	num_token_to_add=lowercase__			)

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


				def 							A					(				self		,	lowercase__		,	lowercase__ = -1		,	lowercase__ = -1		,	lowercase__ = False		,	lowercase__ = None		,	)    ->    Mapping[str, Any]:
									"""simple docstring"""







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

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

									return common_inputs




				def 							A					(				self		,	lowercase__		,	lowercase__		,	lowercase__		,	lowercase__			)    ->    Union[str, Any]:
									"""simple docstring"""







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



def    UpperCamelCase(					lowercase_							)	->				str:





  '''simple docstring'''





  if len(lowercase_							) == 0 or not all(len(lowercase_							) == 2 for pair in coordinates							):
    raise ValueError("""The program cannot work out a fitting polynomial."""							)

  if len({tuple(lowercase_							) for pair in coordinates}							) != len(lowercase_							):
    raise ValueError("""The program cannot work out a fitting polynomial."""							)

  snake_case_       						=      {x for x, _ in coordinates}
  if len(lowercase_							) == 1:
    return f'''x={coordinates[0][0]}'''

  if len(lowercase_							) != len(lowercase_							):
    raise ValueError("""The program cannot work out a fitting polynomial."""							)

  snake_case_       						=      len(lowercase_							)

  snake_case_       						=      0
  snake_case_       						=      []
  # put the x and x to the power values in a matrix
  while count_of_line < x:
    snake_case_       						=      0
    snake_case_       						=      coordinates[count_of_line][0]
    snake_case_       						=      []
    while count_in_line < x:
      count_line.append(a ** (x - (count_in_line + 1))							)
      count_in_line += 1
    matrix.append(lowercase_							)
    count_of_line += 1

  snake_case_       						=      0
  # put the y values into a vector
  snake_case_       						=      []
  while count_of_line < x:
    vector.append(coordinates[count_of_line][1]							)
    count_of_line += 1

  snake_case_       						=      0

  while count < x:
    snake_case_       						=      0
    while zahlen < x:
      if count == zahlen:
        zahlen += 1
      if zahlen == x:
        break
      snake_case_       						=      matrix[zahlen][count] / matrix[count][count]
      for counting_columns, item in enumerate(matrix[count]							):
        # manipulating all the values in the matrix
        matrix[zahlen][counting_columns] -= item * bruch
      # manipulating the values in the vector
      vector[zahlen] -= vector[count] * bruch
      zahlen += 1
    count += 1

  snake_case_       						=      0
  # make solutions
  snake_case_       						=      []
  while count < x:
    solution.append(str(vector[count] / matrix[count][count]							)							)
    count += 1

  snake_case_       						=      0
  snake_case_       						=      """f(x)="""

  while count < x:
    snake_case_       						=      solution[count].split("""E"""							)
    if len(lowercase_							) > 1:
      snake_case_       						=      f'''{remove_e[0]}*10^{remove_e[1]}'''
    solved += f'''x^{x - (count + 1)}*{solution[count]}'''
    if count + 1 != x:
      solved += "+"
    count += 1

  return solved


if __name__ == "__main__":
    print(points_to_polynomial([]))
    print(points_to_polynomial([[]]))
    print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
    print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
    print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
    print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
    print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
    print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
    print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
    print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))