


from __future__ import annotations

from collections.abc import Callable

UpperCamelCase								=	list[list[float | int]]


def   _SCREAMING_SNAKE_CASE	( SCREAMING_SNAKE_CASE ,			SCREAMING_SNAKE_CASE       ):
  A_      :				int		     =					len(SCREAMING_SNAKE_CASE       )
  A_      :				Matrix		     =					[[0 for _ in range(size + 1       )] for _ in range(SCREAMING_SNAKE_CASE       )]
  A_      :				int
  A_      :				int
  A_      :				int
  A_      :				int
  A_      :				int
  A_      :				float

  for row in range(SCREAMING_SNAKE_CASE       ):
    for col in range(SCREAMING_SNAKE_CASE       ):
      A_      :				Optional[Any]		     =					matrix[row][col]

    A_      :				Optional[Any]		     =					vector[row][0]

  A_      :				Dict		     =					0
  A_      :				Union[str, Any]		     =					0
  while row < size and col < size:
    # pivoting
    A_      :				Union[str, Any]		     =					max((abs(augmented[rowa][col]       ), rowa) for rowa in range(SCREAMING_SNAKE_CASE ,			SCREAMING_SNAKE_CASE       )       )[
        1
    ]
    if augmented[pivot_row][col] == 0:
      col += 1
      continue
    else:
      A_     ,       A_      :				Dict		     =					augmented[pivot_row], augmented[row]

    for rowa in range(row + 1 ,			SCREAMING_SNAKE_CASE       ):
      A_      :				Union[str, Any]		     =					augmented[rowa][col] / augmented[row][col]
      A_      :				Optional[Any]		     =					0
      for cola in range(col + 1 ,			size + 1       ):
        augmented[rowa][cola] -= augmented[row][cola] * ratio

    row += 1
    col += 1

  # back substitution
  for col in range(1 ,			SCREAMING_SNAKE_CASE       ):
    for row in range(SCREAMING_SNAKE_CASE       ):
      A_      :				List[Any]		     =					augmented[row][col] / augmented[col][col]
      for cola in range(SCREAMING_SNAKE_CASE ,			size + 1       ):
        augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
  return [
      [round(augmented[row][size] / augmented[row][row] ,			10       )] for row in range(SCREAMING_SNAKE_CASE       )
  ]


def   _SCREAMING_SNAKE_CASE	( SCREAMING_SNAKE_CASE       ):
  A_      :				int		     =					len(SCREAMING_SNAKE_CASE       )
  A_      :				Matrix		     =					[[0 for _ in range(SCREAMING_SNAKE_CASE       )] for _ in range(SCREAMING_SNAKE_CASE       )]
  A_      :				Matrix		     =					[[0] for _ in range(SCREAMING_SNAKE_CASE       )]
  A_      :				Matrix
  A_      :				int
  A_      :				int
  A_      :				int

  for x_val, y_val in enumerate(SCREAMING_SNAKE_CASE       ):
    for col in range(SCREAMING_SNAKE_CASE       ):
      A_      :				Optional[Any]		     =					(x_val + 1) ** (size - col - 1)
    A_      :				Any		     =					y_val

  A_      :				Optional[int]		     =					solve(SCREAMING_SNAKE_CASE ,			SCREAMING_SNAKE_CASE       )

  def interpolated_func(SCREAMING_SNAKE_CASE       ) -> int:
    return sum(
        round(coeffs[x_val][0]       ) * (var ** (size - x_val - 1))
        for x_val in range(SCREAMING_SNAKE_CASE       )       )

  return interpolated_func


def   _SCREAMING_SNAKE_CASE	( SCREAMING_SNAKE_CASE       ):
  return (
      1
      - variable
      + variable**2
      - variable**3
      + variable**4
      - variable**5
      + variable**6
      - variable**7
      + variable**8
      - variable**9
      + variable**10
  )


def   _SCREAMING_SNAKE_CASE	( SCREAMING_SNAKE_CASE = question_function ,			SCREAMING_SNAKE_CASE = 10       ):
  A_      :				list[int]		     =					[func(SCREAMING_SNAKE_CASE       ) for x_val in range(1 ,			order + 1       )]

  A_      :				list[Callable[[int], int]]		     =					[
      interpolate(data_points[:max_coeff]       ) for max_coeff in range(1 ,			order + 1       )
  ]

  A_      :				int		     =					0
  A_      :				Callable[[int], int]
  A_      :				int

  for poly in polynomials:
    A_      :				Tuple		     =					1
    while func(SCREAMING_SNAKE_CASE       ) == poly(SCREAMING_SNAKE_CASE       ):
      x_val += 1

    ret += poly(SCREAMING_SNAKE_CASE       )

  return ret


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








import copy
import tempfile
import unittest

from huggingface_hub import HfFolder, delete_repo
from parameterized import parameterized
from requests.exceptions import HTTPError

from transformers import AutoConfig, GenerationConfig
from transformers.testing_utils import TOKEN, USER, is_staging_test






class   _lowerCamelCase (					unittest.TestCase			):




       """simple docstring"""



       @parameterized.expand([(None,), ('''foo.json''',)]		)
       def        _snake_case       (      self				,       _SCREAMING_SNAKE_CASE		)->Tuple:




         '''simple docstring'''





         A_      :				Dict		     =					GenerationConfig(
             do_sample=_SCREAMING_SNAKE_CASE				,       temperature=0.7				,       length_penalty=1.0				,       bad_words_ids=[[1, 2, 3], [4, 5]]				,       )
         with tempfile.TemporaryDirectory() as tmp_dir:
           config.save_pretrained(_SCREAMING_SNAKE_CASE				,       config_name=_SCREAMING_SNAKE_CASE		)
           A_      :				Tuple		     =					GenerationConfig.from_pretrained(_SCREAMING_SNAKE_CASE				,       config_name=_SCREAMING_SNAKE_CASE		)

         # Checks parameters that were specified
         self.assertEqual(loaded_config.do_sample				,       _SCREAMING_SNAKE_CASE		)
         self.assertEqual(loaded_config.temperature				,       0.7		)
         self.assertEqual(loaded_config.length_penalty				,       1.0		)
         self.assertEqual(loaded_config.bad_words_ids				,       [[1, 2, 3], [4, 5]]		)

         # Checks parameters that were not specified (defaults)
         self.assertEqual(loaded_config.top_k				,       50		)
         self.assertEqual(loaded_config.max_length				,       20		)
         self.assertEqual(loaded_config.max_time				,       _SCREAMING_SNAKE_CASE		)



       def        _snake_case       (      self		)->Dict:




         '''simple docstring'''





         A_      :				str		     =					AutoConfig.from_pretrained('''gpt2'''		)
         A_      :				int		     =					GenerationConfig.from_model_config(_SCREAMING_SNAKE_CASE		)
         A_      :				Dict		     =					GenerationConfig()

         # The generation config has loaded a few non-default parameters from the model config
         self.assertNotEqual(_SCREAMING_SNAKE_CASE				,       _SCREAMING_SNAKE_CASE		)

         # One of those parameters is eos_token_id -- check if it matches
         self.assertNotEqual(generation_config_from_model.eos_token_id				,       default_generation_config.eos_token_id		)
         self.assertEqual(generation_config_from_model.eos_token_id				,       model_config.eos_token_id		)



       def        _snake_case       (      self		)->Optional[int]:




         '''simple docstring'''





         A_      :				List[Any]		     =					GenerationConfig()
         A_      :				Optional[Any]		     =					{
             '''max_new_tokens''': 1024,
             '''foo''': '''bar''',
         }
         A_      :				Dict		     =					copy.deepcopy(_SCREAMING_SNAKE_CASE		)
         A_      :				Optional[int]		     =					generation_config.update(**_SCREAMING_SNAKE_CASE		)

         # update_kwargs was not modified (no side effects)
         self.assertEqual(_SCREAMING_SNAKE_CASE				,       _SCREAMING_SNAKE_CASE		)

         # update_kwargs was used to update the config on valid attributes
         self.assertEqual(generation_config.max_new_tokens				,       1024		)

         # `.update()` returns a dictionary of unused kwargs
         self.assertEqual(_SCREAMING_SNAKE_CASE				,       {'''foo''': '''bar'''}		)



       def        _snake_case       (      self		)->str:




         '''simple docstring'''





         A_      :				List[str]		     =					GenerationConfig()
         A_      :				int		     =					'''bar'''

         with tempfile.TemporaryDirectory('''test-generation-config'''		) as tmp_dir:
           generation_config.save_pretrained(_SCREAMING_SNAKE_CASE		)

           A_      :				Optional[Any]		     =					GenerationConfig.from_pretrained(_SCREAMING_SNAKE_CASE		)
         # update_kwargs was used to update the config on valid attributes
         self.assertEqual(new_config.foo				,       '''bar'''		)

         A_      :				Optional[int]		     =					GenerationConfig.from_model_config(_SCREAMING_SNAKE_CASE		)
         assert not hasattr(_SCREAMING_SNAKE_CASE				,       '''foo'''		)  # no new kwargs should be initialized if from config







       def        _snake_case       (      self		)->List[Any]:




         '''simple docstring'''





         A_      :				str		     =					GenerationConfig()
         self.assertEqual(default_config.temperature				,       1.0		)
         self.assertEqual(default_config.do_sample				,       _SCREAMING_SNAKE_CASE		)
         self.assertEqual(default_config.num_beams				,       1		)

         A_      :				str		     =					GenerationConfig(
             do_sample=_SCREAMING_SNAKE_CASE				,       temperature=0.7				,       length_penalty=1.0				,       bad_words_ids=[[1, 2, 3], [4, 5]]				,       )
         self.assertEqual(config.temperature				,       0.7		)
         self.assertEqual(config.do_sample				,       _SCREAMING_SNAKE_CASE		)
         self.assertEqual(config.num_beams				,       1		)

         with tempfile.TemporaryDirectory() as tmp_dir:
           config.save_pretrained(_SCREAMING_SNAKE_CASE		)
           A_      :				Dict		     =					GenerationConfig.from_pretrained(_SCREAMING_SNAKE_CASE				,       temperature=1.0		)

         self.assertEqual(loaded_config.temperature				,       1.0		)
         self.assertEqual(loaded_config.do_sample				,       _SCREAMING_SNAKE_CASE		)
         self.assertEqual(loaded_config.num_beams				,       1		)  # default value






@is_staging_test
class   _lowerCamelCase (					unittest.TestCase			):




       """simple docstring"""



       @classmethod
       def        _snake_case       (      cls		)->Optional[int]:




         '''simple docstring'''





         A_      :				str		     =					TOKEN
         HfFolder.save_token(_SCREAMING_SNAKE_CASE		)



       @classmethod
       def        _snake_case       (      cls		)->List[Any]:




         '''simple docstring'''





         try:
           delete_repo(token=cls._token				,       repo_id='''test-generation-config'''		)
         except HTTPError:
           pass

         try:
           delete_repo(token=cls._token				,       repo_id='''valid_org/test-generation-config-org'''		)
         except HTTPError:
           pass



       def        _snake_case       (      self		)->List[Any]:




         '''simple docstring'''





         A_      :				List[Any]		     =					GenerationConfig(
             do_sample=_SCREAMING_SNAKE_CASE				,       temperature=0.7				,       length_penalty=1.0				,       )
         config.push_to_hub('''test-generation-config'''				,       use_auth_token=self._token		)

         A_      :				Optional[int]		     =					GenerationConfig.from_pretrained(F'''{USER}/test-generation-config'''		)
         for k, v in config.to_dict().items():
           if k != "transformers_version":
             self.assertEqual(_SCREAMING_SNAKE_CASE				,       getattr(_SCREAMING_SNAKE_CASE				,       _SCREAMING_SNAKE_CASE		)		)

        # Reset repo
         delete_repo(token=self._token				,       repo_id='''test-generation-config'''		)

         # Push to hub via save_pretrained
         with tempfile.TemporaryDirectory() as tmp_dir:
           config.save_pretrained(
               _SCREAMING_SNAKE_CASE				,       repo_id='''test-generation-config'''				,       push_to_hub=_SCREAMING_SNAKE_CASE				,       use_auth_token=self._token		)

         A_      :				Optional[Any]		     =					GenerationConfig.from_pretrained(F'''{USER}/test-generation-config'''		)
         for k, v in config.to_dict().items():
           if k != "transformers_version":
             self.assertEqual(_SCREAMING_SNAKE_CASE				,       getattr(_SCREAMING_SNAKE_CASE				,       _SCREAMING_SNAKE_CASE		)		)







       def        _snake_case       (      self		)->List[str]:




         '''simple docstring'''





         A_      :				Tuple		     =					GenerationConfig(
             do_sample=_SCREAMING_SNAKE_CASE				,       temperature=0.7				,       length_penalty=1.0				,       )
         config.push_to_hub('''valid_org/test-generation-config-org'''				,       use_auth_token=self._token		)

         A_      :				Union[str, Any]		     =					GenerationConfig.from_pretrained('''valid_org/test-generation-config-org'''		)
         for k, v in config.to_dict().items():
           if k != "transformers_version":
             self.assertEqual(_SCREAMING_SNAKE_CASE				,       getattr(_SCREAMING_SNAKE_CASE				,       _SCREAMING_SNAKE_CASE		)		)

        # Reset repo
         delete_repo(token=self._token				,       repo_id='''valid_org/test-generation-config-org'''		)

         # Push to hub via save_pretrained
         with tempfile.TemporaryDirectory() as tmp_dir:
           config.save_pretrained(
               _SCREAMING_SNAKE_CASE				,       repo_id='''valid_org/test-generation-config-org'''				,       push_to_hub=_SCREAMING_SNAKE_CASE				,       use_auth_token=self._token		)

         A_      :				Dict		     =					GenerationConfig.from_pretrained('''valid_org/test-generation-config-org'''		)
         for k, v in config.to_dict().items():
           if k != "transformers_version":
             self.assertEqual(_SCREAMING_SNAKE_CASE				,       getattr(_SCREAMING_SNAKE_CASE				,       _SCREAMING_SNAKE_CASE		)		)




