




"""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


__lowerCamelCase								=						logging.get_logger(__name__)

__lowerCamelCase								=						{
    "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  _snake_case				(							A__       ):

    '''simple docstring'''




    UpperCamelCase__		     ="""mbart"""
    UpperCamelCase__		     =["""past_key_values"""]
    UpperCamelCase__		     ={"""num_attention_heads""": """encoder_attention_heads""", """hidden_size""": """d_model"""}





    def __init__(							self      :  Union[str, Any]					,							snake_case      :  Optional[int]=50_265					,							snake_case      :  List[str]=1_024					,							snake_case      :  List[str]=12					,							snake_case      :  Tuple=4_096					,							snake_case      :  Tuple=16					,							snake_case      :  Dict=12					,							snake_case      :  List[str]=4_096					,							snake_case      :  int=16					,							snake_case      :  int=0.0					,							snake_case      :  Tuple=0.0					,							snake_case      :  Dict=True					,							snake_case      :  Optional[Any]=True					,							snake_case      :  str="gelu"					,							snake_case      :  Optional[int]=1_024					,							snake_case      :  Any=0.1					,							snake_case      :  str=0.0					,							snake_case      :  Tuple=0.0					,							snake_case      :  List[Any]=0.02					,							snake_case      :  List[Any]=0.0					,							snake_case      :  List[Any]=False					,							snake_case      :  List[Any]=1					,							snake_case      :  Tuple=0					,							snake_case      :  List[Any]=2					,							snake_case      :  Any=2					,							**snake_case      :  Tuple					,							):
        UpperCAmelCase_					:str      			=      vocab_size
        UpperCAmelCase_					:Any      			=      max_position_embeddings
        UpperCAmelCase_					:Tuple      			=      d_model
        UpperCAmelCase_					:Union[str, Any]      			=      encoder_ffn_dim
        UpperCAmelCase_					:Optional[Any]      			=      encoder_layers
        UpperCAmelCase_					:Tuple      			=      encoder_attention_heads
        UpperCAmelCase_					:List[Any]      			=      decoder_ffn_dim
        UpperCAmelCase_					:Optional[Any]      			=      decoder_layers
        UpperCAmelCase_					:int      			=      decoder_attention_heads
        UpperCAmelCase_					:Optional[int]      			=      dropout
        UpperCAmelCase_					:List[Any]      			=      attention_dropout
        UpperCAmelCase_					:str      			=      activation_dropout
        UpperCAmelCase_					:Any      			=      activation_function
        UpperCAmelCase_					:Optional[int]      			=      init_std
        UpperCAmelCase_					:Optional[int]      			=      encoder_layerdrop
        UpperCAmelCase_					:List[Any]      			=      decoder_layerdrop
        UpperCAmelCase_					:Dict      			=      classifier_dropout
        UpperCAmelCase_					:int      			=      use_cache
        UpperCAmelCase_					:Optional[Any]      			=      encoder_layers
        UpperCAmelCase_					:List[Any]      			=      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					,							forced_eos_token_id=snake_case					,							**snake_case					,							)



class  _snake_case				(							A__       ):

    '''simple docstring'''




    @property
    def 				snake_case_ (							self      :  int     ):
        if self.task in ["default", "seq2seq-lm"]:
            UpperCAmelCase_					:List[Any]      			=      OrderedDict(
                [
                    ('''input_ids''', {0: '''batch''', 1: '''encoder_sequence'''}),
                    ('''attention_mask''', {0: '''batch''', 1: '''encoder_sequence'''}),
                ]     )

            if self.use_past:
                UpperCAmelCase_					:Optional[int]      			=      {0: '''batch'''}
                UpperCAmelCase_					:Tuple      			=      {0: '''batch''', 1: '''past_decoder_sequence + sequence'''}
            else:
                UpperCAmelCase_					:List[str]      			=      {0: '''batch''', 1: '''decoder_sequence'''}
                UpperCAmelCase_					:Dict      			=      {0: '''batch''', 1: '''decoder_sequence'''}

            if self.use_past:
                self.fill_with_past_key_values_(snake_case					,							direction='''inputs'''     )
        elif self.task == "causal-lm":
            # TODO: figure this case out.
            UpperCAmelCase_					:Tuple      			=      OrderedDict(
                [
                    ('''input_ids''', {0: '''batch''', 1: '''encoder_sequence'''}),
                    ('''attention_mask''', {0: '''batch''', 1: '''encoder_sequence'''}),
                ]     )
            if self.use_past:
                UpperCAmelCase_					:str      			=      self.num_layers
                for i in range(snake_case     ):
                    UpperCAmelCase_					:List[str]      			=      {0: '''batch''', 2: '''past_sequence + sequence'''}
                    UpperCAmelCase_					:List[Any]      			=      {0: '''batch''', 2: '''past_sequence + sequence'''}
        else:
            UpperCAmelCase_					:int      			=      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 				snake_case_ (							self      :  Union[str, Any]     ):
        if self.task in ["default", "seq2seq-lm"]:
            UpperCAmelCase_					:int      			=      super().outputs
        else:
            UpperCAmelCase_					:Optional[int]      			=      super(snake_case					,							self     ).outputs
            if self.use_past:
                UpperCAmelCase_					:List[str]      			=      self.num_layers
                for i in range(snake_case     ):
                    UpperCAmelCase_					:Dict      			=      {0: '''batch''', 2: '''past_sequence + sequence'''}
                    UpperCAmelCase_					:Tuple      			=      {0: '''batch''', 2: '''past_sequence + sequence'''}
        return common_outputs





    def 				snake_case_ (							self      :  Union[str, Any]					,							snake_case      :  PreTrainedTokenizer					,							snake_case      :  int = -1					,							snake_case      :  int = -1					,							snake_case      :  bool = False					,							snake_case      :  Optional[TensorType] = None					,							):
        UpperCAmelCase_					:Dict      			=      self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
            snake_case					,							snake_case					,							snake_case					,							snake_case					,							snake_case     )

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

            UpperCAmelCase_					:Union[str, Any]      			=      torch.cat(
                [common_inputs['''decoder_attention_mask'''], torch.ones(snake_case					,							snake_case     )]					,							dim=1     )

            UpperCAmelCase_					:Union[str, Any]      			=      []
            # If the number of encoder and decoder layers are present in the model configuration, both are considered
            UpperCAmelCase_					:List[Any]      			=      self.num_layers
            UpperCAmelCase_					:Any      			=      min(snake_case					,							snake_case     )
            UpperCAmelCase_					:Optional[Any]      			=      max(snake_case					,							snake_case     ) - min_num_layers
            UpperCAmelCase_					:List[Any]      			=      '''encoder''' if num_encoder_layers > num_decoder_layers else '''decoder'''

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





    def 				snake_case_ (							self      :  Tuple					,							snake_case      :  PreTrainedTokenizer					,							snake_case      :  int = -1					,							snake_case      :  int = -1					,							snake_case      :  bool = False					,							snake_case      :  Optional[TensorType] = None					,							):
        UpperCAmelCase_					:List[Any]      			=      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
            UpperCAmelCase_					:Union[str, Any]      			=      common_inputs['''input_ids'''].shape
            # Not using the same length for past_key_values
            UpperCAmelCase_					:Dict      			=      seqlen + 2
            UpperCAmelCase_					:Optional[int]      			=      self.num_layers
            UpperCAmelCase_					:Any      			=      self.num_attention_heads
            UpperCAmelCase_					:Tuple      			=      (
                batch,
                num_encoder_attention_heads,
                past_key_values_length,
                self._config.hidden_size // num_encoder_attention_heads,
            )

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





    def 				snake_case_ (							self      :  Tuple					,							snake_case      :  PreTrainedTokenizer					,							snake_case      :  int = -1					,							snake_case      :  int = -1					,							snake_case      :  bool = False					,							snake_case      :  Optional[TensorType] = None					,							):
        # Copied from OnnxConfig.generate_dummy_inputs
        # Did not use super(OnnxConfigWithPast, self).generate_dummy_inputs for code clarity.
        # If dynamic axis (-1) we forward with a fixed dimension of 2 samples to avoid optimizations made by ONNX
        UpperCAmelCase_					:Optional[Any]      			=      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
        UpperCAmelCase_					:Tuple      			=      tokenizer.num_special_tokens_to_add(snake_case     )
        UpperCAmelCase_					:Optional[Any]      			=      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
        UpperCAmelCase_					:List[Any]      			=      [''' '''.join([tokenizer.unk_token]     ) * seq_length] * batch_size
        UpperCAmelCase_					:Tuple      			=      dict(tokenizer(snake_case					,							return_tensors=snake_case     )     )
        return common_inputs





    def 				snake_case_ (							self      :  Dict					,							snake_case      :  PreTrainedTokenizer					,							snake_case      :  int = -1					,							snake_case      :  int = -1					,							snake_case      :  bool = False					,							snake_case      :  Optional[TensorType] = None					,							):
        if self.task in ["default", "seq2seq-lm"]:
            UpperCAmelCase_					:Tuple      			=      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":
            UpperCAmelCase_					:Any      			=      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:
            UpperCAmelCase_					:List[Any]      			=      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 				snake_case_ (							self      :  List[Any]					,							snake_case      :  int					,							snake_case      :  Dict					,							snake_case      :  Optional[int]					,							snake_case      :  Optional[int]     ):
        if self.task in ["default", "seq2seq-lm"]:
            UpperCAmelCase_					:Optional[Any]      			=      super()._flatten_past_key_values_(snake_case					,							snake_case					,							snake_case					,							snake_case     )
        else:
            UpperCAmelCase_					:Optional[Any]      			=      super(snake_case					,							self     )._flatten_past_key_values_(
                snake_case					,							snake_case					,							snake_case					,							snake_case     )








"""simple docstring"""

def 				a (						__snake_case     :				list[list[int]]  ):



				'''simple docstring'''





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

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

				UpperCAmelCase_					:Optional[Any]      			=      {x for x, _ in coordinates}
				if len(__snake_case  ) == 1:
								return f'x={coordinates[0][0]}'

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

				UpperCAmelCase_					:List[Any]      			=      len(__snake_case  )

				UpperCAmelCase_					:str      			=      0
				UpperCAmelCase_					:list[list[float]]      			=      []
				# put the x and x to the power values in a matrix
				while count_of_line < x:
								UpperCAmelCase_					:str      			=      0
								UpperCAmelCase_					:Optional[int]      			=      coordinates[count_of_line][0]
								UpperCAmelCase_					:list[float]      			=      []
								while count_in_line < x:
												count_line.append(a ** (x - (count_in_line + 1))  )
												count_in_line += 1
								matrix.append(__snake_case  )
								count_of_line += 1

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

				UpperCAmelCase_					:Dict      			=      0

				while count < x:
								UpperCAmelCase_					:Any      			=      0
								while zahlen < x:
												if count == zahlen:
																zahlen += 1
												if zahlen == x:
																break
												UpperCAmelCase_					:str      			=      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

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

				UpperCAmelCase_					:Optional[int]      			=      0
				UpperCAmelCase_					:Optional[Any]      			=      '''f(x)='''

				while count < x:
								UpperCAmelCase_					:list[str]      			=      solution[count].split('''E'''  )
								if len(__snake_case  ) > 1:
												UpperCAmelCase_					:List[Any]      			=      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]]))


