code: 
  
  
  
  
  
  
  from collections import OrderedDict
  from typing import Any, List, Mapping, Optional
  
  from ... import PreTrainedTokenizer, TensorType, is_torch_available
  from ...configuration_utils import PretrainedConfig
  from ...onnx import OnnxConfigWithPast, PatchingSpec
  from ...utils import logging
  
  
  lowerCamelCase			:							Tuple       =logging.get_logger(__name__)
  
  lowerCamelCase			:							Any       ={
      '''gpt2''': '''https://huggingface.co/gpt2/resolve/main/config.json''',
      '''gpt2-medium''': '''https://huggingface.co/gpt2-medium/resolve/main/config.json''',
      '''gpt2-large''': '''https://huggingface.co/gpt2-large/resolve/main/config.json''',
      '''gpt2-xl''': '''https://huggingface.co/gpt2-xl/resolve/main/config.json''',
      '''distilgpt2''': '''https://huggingface.co/distilgpt2/resolve/main/config.json''',
  }
  
  
  
  
  
  class     __a						(					A__ ):
   _lowerCAmelCase : Optional[Any] 				=				'''gpt2'''
   _lowerCAmelCase : List[Any] 				=				['''past_key_values''']
   _lowerCAmelCase : str 				=				{
       '''hidden_size''': '''n_embd''',
       '''max_position_embeddings''': '''n_positions''',
       '''num_attention_heads''': '''n_head''',
       '''num_hidden_layers''': '''n_layer''',
   }
  
  
  
  
  
  
  
   def __init__(	self      :     Tuple							,     SCREAMING_SNAKE_CASE      :     str=5_02_57							,     SCREAMING_SNAKE_CASE      :     Optional[int]=10_24							,     SCREAMING_SNAKE_CASE      :     int=7_68							,     SCREAMING_SNAKE_CASE      :     Dict=12							,     SCREAMING_SNAKE_CASE      :     str=12							,     SCREAMING_SNAKE_CASE      :     List[Any]=None							,     SCREAMING_SNAKE_CASE      :     Union[str, Any]="gelu_new"							,     SCREAMING_SNAKE_CASE      :     Optional[int]=0.1							,     SCREAMING_SNAKE_CASE      :     Union[str, Any]=0.1							,     SCREAMING_SNAKE_CASE      :     Union[str, Any]=0.1							,     SCREAMING_SNAKE_CASE      :     List[Any]=1e-5							,     SCREAMING_SNAKE_CASE      :     Optional[Any]=0.0_2							,     SCREAMING_SNAKE_CASE      :     Dict="cls_index"							,     SCREAMING_SNAKE_CASE      :     Optional[Any]=True							,     SCREAMING_SNAKE_CASE      :     Tuple=None							,     SCREAMING_SNAKE_CASE      :     Any=True							,     SCREAMING_SNAKE_CASE      :     Any=0.1							,     SCREAMING_SNAKE_CASE      :     int=True							,     SCREAMING_SNAKE_CASE      :     List[str]=True							,     SCREAMING_SNAKE_CASE      :     List[str]=5_02_56							,     SCREAMING_SNAKE_CASE      :     List[str]=5_02_56							,     SCREAMING_SNAKE_CASE      :     Optional[int]=False							,     SCREAMING_SNAKE_CASE      :     Optional[Any]=False							,     **SCREAMING_SNAKE_CASE      :     int							,     ):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        UpperCamelCase__    :     Union[str, Any]        =						vocab_size
        UpperCamelCase__    :     Any        =						n_positions
        UpperCamelCase__    :     Optional[Any]        =						n_embd
        UpperCamelCase__    :     Any        =						n_layer
        UpperCamelCase__    :     Dict        =						n_head
        UpperCamelCase__    :     Dict        =						n_inner
        UpperCamelCase__    :     Any        =						activation_function
        UpperCamelCase__    :     Tuple        =						resid_pdrop
        UpperCamelCase__    :     Tuple        =						embd_pdrop
        UpperCamelCase__    :     Dict        =						attn_pdrop
        UpperCamelCase__    :     str        =						layer_norm_epsilon
        UpperCamelCase__    :     Any        =						initializer_range
        UpperCamelCase__    :     Dict        =						summary_type
        UpperCamelCase__    :     Tuple        =						summary_use_proj
        UpperCamelCase__    :     str        =						summary_activation
        UpperCamelCase__    :     Dict        =						summary_first_dropout
        UpperCamelCase__    :     Optional[int]        =						summary_proj_to_labels
        UpperCamelCase__    :     Optional[Any]        =						scale_attn_weights
        UpperCamelCase__    :     List[Any]        =						use_cache
        UpperCamelCase__    :     Dict        =						scale_attn_by_inverse_layer_idx
        UpperCamelCase__    :     List[Any]        =						reorder_and_upcast_attn
  
        UpperCamelCase__    :     int        =						bos_token_id
        UpperCamelCase__    :     Dict        =						eos_token_id
  
        super().__init__(bos_token_id=SCREAMING_SNAKE_CASE							,     eos_token_id=SCREAMING_SNAKE_CASE							,     **SCREAMING_SNAKE_CASE		)
  
  
  
  
  
  
  
  class     __a						(					A__ ):
  
  
  
  
  
  
  
   def __init__(	self      :     Dict							,     SCREAMING_SNAKE_CASE      :     PretrainedConfig							,     SCREAMING_SNAKE_CASE      :     str = "default"							,     SCREAMING_SNAKE_CASE      :     List[PatchingSpec] = None							,     SCREAMING_SNAKE_CASE      :     bool = False							,     ):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        super().__init__(SCREAMING_SNAKE_CASE							,     task=SCREAMING_SNAKE_CASE							,     patching_specs=SCREAMING_SNAKE_CASE							,     use_past=SCREAMING_SNAKE_CASE		)
        if not getattr(self._config							,     "pad_token_id"							,     SCREAMING_SNAKE_CASE		):
             # TODO: how to do that better?
             UpperCamelCase__    :     List[str]        =						0
  
  
  
  
  
  
  
   @property
   def       __lowercase      (	self      :     int		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        UpperCamelCase__    :     Union[str, Any]        =						OrderedDict({"input_ids": {0: "batch", 1: "sequence"}}		)
        if self.use_past:
             self.fill_with_past_key_values_(SCREAMING_SNAKE_CASE							,     direction="inputs"		)
             UpperCamelCase__    :     int        =						{0: "batch", 1: "past_sequence + sequence"}
        else:
             UpperCamelCase__    :     List[Any]        =						{0: "batch", 1: "sequence"}
  
        return common_inputs
  
  
  
  
  
  
  
   @property
   def       __lowercase      (	self      :     Union[str, Any]		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        return self._config.n_layer
  
  
  
  
  
  
  
   @property
   def       __lowercase      (	self      :     Dict		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        return self._config.n_head
  
  
  
  
  
  
  
   def       __lowercase      (	self      :     Any							,     SCREAMING_SNAKE_CASE      :     PreTrainedTokenizer							,     SCREAMING_SNAKE_CASE      :     int = -1							,     SCREAMING_SNAKE_CASE      :     int = -1							,     SCREAMING_SNAKE_CASE      :     bool = False							,     SCREAMING_SNAKE_CASE      :     Optional[TensorType] = None							,     ):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        UpperCamelCase__    :     int        =						super(SCREAMING_SNAKE_CASE							,     self		).generate_dummy_inputs(
            SCREAMING_SNAKE_CASE							,     batch_size=SCREAMING_SNAKE_CASE							,     seq_length=SCREAMING_SNAKE_CASE							,     is_pair=SCREAMING_SNAKE_CASE							,     framework=SCREAMING_SNAKE_CASE		)
  
        # We need to order the input in the way they appears in the forward()
        UpperCamelCase__    :     Union[str, Any]        =						OrderedDict({"input_ids": common_inputs["input_ids"]}		)
  
        # Need to add the past_keys
        if self.use_past:
             if not is_torch_available():
                  raise ValueError("Cannot generate dummy past_keys inputs without PyTorch installed."		)
             else:
                  import torch
  
                  UpperCamelCase__       ,  UpperCamelCase__    :     Optional[int]        =						common_inputs["input_ids"].shape
                  # Not using the same length for past_key_values
                  UpperCamelCase__    :     List[Any]        =						seqlen + 2
                  UpperCamelCase__    :     str        =						(
                      batch,
                      self.num_attention_heads,
                      past_key_values_length,
                      self._config.hidden_size // self.num_attention_heads,
                  )
                  UpperCamelCase__    :     str        =						[
                      (torch.zeros(SCREAMING_SNAKE_CASE		), torch.zeros(SCREAMING_SNAKE_CASE		)) for _ in range(self.num_layers		)
                  ]
  
        UpperCamelCase__    :     Tuple        =						common_inputs["attention_mask"]
        if self.use_past:
             UpperCamelCase__    :     str        =						ordered_inputs["attention_mask"].dtype
             UpperCamelCase__    :     Optional[Any]        =						torch.cat(
                 [ordered_inputs["attention_mask"], torch.ones(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE							,     dtype=SCREAMING_SNAKE_CASE		)]							,     dim=1		)
  
        return ordered_inputs
  
  
  
  
  
  
  
   @property
   def       __lowercase      (	self      :     Any		):
  
  
        '''simple docstring'''
  
  
  
  
  
  
        return 13
style_context: 
  
  
  
  
  
  
  def 	SCREAMING_SNAKE_CASE							(      __lowerCAmelCase    )				->			str:
       if len(__lowerCAmelCase    ) == 0 or not all(len(__lowerCAmelCase    ) == 2 for pair in coordinates    ):
            raise ValueError("The program cannot work out a fitting polynomial."    )
  
       if len({tuple(__lowerCAmelCase    ) for pair in coordinates}    ) != len(__lowerCAmelCase    ):
            raise ValueError("The program cannot work out a fitting polynomial."    )
  
       UpperCamelCase__    :     List[str]        =						{x for x, _ in coordinates}
       if len(__lowerCAmelCase    ) == 1:
            return f'x={coordinates[0][0]}'
  
       if len(__lowerCAmelCase    ) != len(__lowerCAmelCase    ):
            raise ValueError("The program cannot work out a fitting polynomial."    )
  
       UpperCamelCase__    :     Any        =						len(__lowerCAmelCase    )
  
       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__    :     int        =						0
            UpperCamelCase__    :     List[Any]        =						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(__lowerCAmelCase    )
            count_of_line += 1
  
       UpperCamelCase__    :     List[Any]        =						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__    :     Tuple        =						0
  
       while count < x:
            UpperCamelCase__    :     Dict        =						0
            while zahlen < x:
                 if count == zahlen:
                      zahlen += 1
                 if zahlen == x:
                      break
                 UpperCamelCase__    :     Optional[Any]        =						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__    :     int        =						0
       UpperCamelCase__    :     List[str]        =						"f(x)="
  
       while count < x:
            UpperCamelCase__    :     list[str]        =						solution[count].split("E"    )
            if len(__lowerCAmelCase    ) > 1:
                 UpperCamelCase__    :     Union[str, 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]]))