

'''simple docstring'''




def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   list[list[int]]						):
  if len(SCREAMING_SNAKE_CASE						) == 0 or not all(len(SCREAMING_SNAKE_CASE						) == 2 for pair in coordinates						):
    raise ValueError('The program cannot work out a fitting polynomial.'						)

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

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

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

  UpperCAmelCase													=	len(SCREAMING_SNAKE_CASE						)

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

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

  UpperCAmelCase													=	0

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

  UpperCAmelCase													=	0
  UpperCAmelCase													=	'f(x)='

  while count < x:
    UpperCAmelCase													=	solution[count].split('E'						)
    if len(SCREAMING_SNAKE_CASE						) > 1:
      UpperCAmelCase													=	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]]))





'''simple docstring'''




from collections import OrderedDict
from typing import Mapping

from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfig
from ...utils import logging


_a				: Optional[int] 							=						logging.get_logger(__name__)

_a				: Dict 							=						{
    'mnaylor/mega-base-wikitext': 'https://huggingface.co/mnaylor/mega-base-wikitext/resolve/main/config.json',
}



class        lowercase_	(		a ):

  '''simple docstring'''





  __lowerCAmelCase					: List[str]      =   "mega"
  def __init__(     self   , a_=3_0_5_2_2   , a_=1_2_8   , a_=4   , a_=2_5_6   , a_=1_6   , a_=True   , a_=6_4   , a_=False   , a_=-1   , a_=None   , a_=True   , a_="scalenorm"   , a_=True   , a_="silu"   , a_="softmax"   , a_=0.1   , a_=0.1   , a_=0.1   , a_=False   , a_=True   , a_=2_5_6   , a_=True   , a_=0.1   , a_=2_0_4_8   , a_=False   , a_=2   , a_=0.02   , a_=0.2   , a_=0.02   , a_=1.0   , a_=1   , a_=0   , a_=2   , a_="rotary"   , a_=None   , a_=True   , a_=True   , **a_   , )							->				Any:


    """simple docstring"""
    super().__init__(pad_token_id=a_   , bos_token_id=a_   , eos_token_id=a_   , **a_     )

    UpperCAmelCase													=	vocab_size
    UpperCAmelCase													=	hidden_size
    UpperCAmelCase													=	num_hidden_layers
    UpperCAmelCase													=	activation
    UpperCAmelCase													=	attention_activation
    UpperCAmelCase													=	intermediate_size
    UpperCAmelCase													=	ema_projection_size
    UpperCAmelCase													=	bidirectional
    UpperCAmelCase													=	shared_representation_size
    UpperCAmelCase													=	use_chunking
    UpperCAmelCase													=	chunk_size
    UpperCAmelCase													=	truncation
    UpperCAmelCase													=	normalize_before_mega
    UpperCAmelCase													=	normalization_type
    UpperCAmelCase													=	norm_affine
    UpperCAmelCase													=	dropout_prob
    UpperCAmelCase													=	hidden_dropout_prob
    UpperCAmelCase													=	attention_probs_dropout_prob
    UpperCAmelCase													=	use_feature_dropout
    UpperCAmelCase													=	use_normalized_ffn
    UpperCAmelCase													=	nffn_hidden_size
    UpperCAmelCase													=	normalize_before_ffn
    UpperCAmelCase													=	nffn_activation_dropout_prob
    UpperCAmelCase													=	max_positions
    UpperCAmelCase													=	add_token_type_embeddings
    UpperCAmelCase													=	type_vocab_size
    UpperCAmelCase													=	initializer_range
    UpperCAmelCase													=	ema_delta_alpha_range
    UpperCAmelCase													=	ema_beta_range
    UpperCAmelCase													=	ema_gamma_omega_range
    UpperCAmelCase													=	relative_positional_bias
    UpperCAmelCase													=	use_cache
    UpperCAmelCase													=	classifier_dropout
    UpperCAmelCase													=	add_lm_hidden_dense_layer
    UpperCAmelCase													=	1  # not used but required by Hugging Face




class        lowercase_	(		a ):

  '''simple docstring'''





  @property
  def 						snake_case_			(     self     )							->				Mapping[str, Mapping[int, str]]:


    """simple docstring"""
    if self.task == "multiple-choice":
      UpperCAmelCase													=	{0: 'batch', 1: 'choice', 2: 'sequence'}
    else:
      UpperCAmelCase													=	{0: 'batch', 1: 'sequence'}
    return OrderedDict(
        [
            ('input_ids', dynamic_axis),
            ('attention_mask', dynamic_axis),
        ]     )


