


from __future__ import annotations

from collections.abc import Callable

__snake_case   							=						list[list[float | int]]






def 		_A		(		_lowercase					,  _lowercase )					-> Matrix:


     """simple docstring"""


     __UpperCamelCase =			len(_lowercase )
     __UpperCamelCase =			[[0 for _ in range(size + 1 )] for _ in range(_lowercase )]
     __UpperCamelCase =			42
     __UpperCamelCase =			42
     __UpperCamelCase =			42
     __UpperCamelCase =			42
     __UpperCamelCase =			42
     __UpperCamelCase =			42

     for row in range(_lowercase ):
          for col in range(_lowercase ):
               __UpperCamelCase =			matrix[row][col]

          __UpperCamelCase =			vector[row][0]

     __UpperCamelCase =			0
     __UpperCamelCase =			0
     while row < size and col < size:
          # pivoting
          __UpperCamelCase =			max((abs(augmented[rowa][col] ), rowa) for rowa in range(_lowercase					,  _lowercase ) )[
              1
          ]
          if augmented[pivot_row][col] == 0:
               col += 1
               continue
          else:
               __UpperCamelCase,    __UpperCamelCase =			augmented[pivot_row], augmented[row]

          for rowa in range(row + 1					,  _lowercase ):
               __UpperCamelCase =			augmented[rowa][col] / augmented[row][col]
               __UpperCamelCase =			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					,  _lowercase ):
          for row in range(_lowercase ):
               __UpperCamelCase =			augmented[row][col] / augmented[col][col]
               for cola in range(_lowercase					,  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(_lowercase )
     ]






def 		_A		(		_lowercase )					-> Callable[[int], int]:


     """simple docstring"""


     __UpperCamelCase =			len(_lowercase )
     __UpperCamelCase =			[[0 for _ in range(_lowercase )] for _ in range(_lowercase )]
     __UpperCamelCase =			[[0] for _ in range(_lowercase )]
     __UpperCamelCase =			42
     __UpperCamelCase =			42
     __UpperCamelCase =			42
     __UpperCamelCase =			42

     for x_val, y_val in enumerate(_lowercase ):
          for col in range(_lowercase ):
               __UpperCamelCase =			(x_val + 1) ** (size - col - 1)
          __UpperCamelCase =			y_val

     __UpperCamelCase =			solve(_lowercase					,  _lowercase )

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

     return interpolated_func






def 		_A		(		_lowercase )					-> int:


     """simple docstring"""


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






def 		_A		(		_lowercase = question_function					,  _lowercase = 10 )					-> int:


     """simple docstring"""


     __UpperCamelCase =			[func(_lowercase ) for x_val in range(1					,  order + 1 )]

     __UpperCamelCase =			[
         interpolate(data_points[:max_coeff] ) for max_coeff in range(1					,  order + 1 )
     ]

     __UpperCamelCase =			0
     __UpperCamelCase =			42
     __UpperCamelCase =			42

     for poly in polynomials:
          __UpperCamelCase =			1
          while func(_lowercase ) == poly(_lowercase ):
               x_val += 1

          ret += poly(_lowercase )

     return ret


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






import pytest

import datasets


# Import fixture modules as plugins
__snake_case   							=						['''tests.fixtures.files''', '''tests.fixtures.hub''', '''tests.fixtures.fsspec''']






def 		_A		(		_lowercase					,  _lowercase )					-> Tuple:


     """simple docstring"""


     for item in items:
          if any(marker in item.keywords for marker in ['integration', 'unit'] ):
               continue
          item.add_marker(pytest.mark.unit )






def 		_A		(		_lowercase )					-> str:


     """simple docstring"""


     config.addinivalue_line('markers'					,  'torchaudio_latest: mark test to run with torchaudio>=0.12' )






@pytest.fixture(autouse=_lowercase )
def 		_A		(		_lowercase					,  _lowercase )					-> Any:


     """simple docstring"""


     __UpperCamelCase =			tmp_path_factory.getbasetemp() / 'cache'
     __UpperCamelCase =			test_hf_cache_home / 'datasets'
     __UpperCamelCase =			test_hf_cache_home / 'metrics'
     __UpperCamelCase =			test_hf_cache_home / 'modules'
     monkeypatch.setattr('datasets.config.HF_DATASETS_CACHE'					,  str(_lowercase ) )
     monkeypatch.setattr('datasets.config.HF_METRICS_CACHE'					,  str(_lowercase ) )
     monkeypatch.setattr('datasets.config.HF_MODULES_CACHE'					,  str(_lowercase ) )
     __UpperCamelCase =			test_hf_datasets_cache / 'downloads'
     monkeypatch.setattr('datasets.config.DOWNLOADED_DATASETS_PATH'					,  str(_lowercase ) )
     __UpperCamelCase =			test_hf_datasets_cache / 'downloads' / 'extracted'
     monkeypatch.setattr('datasets.config.EXTRACTED_DATASETS_PATH'					,  str(_lowercase ) )






@pytest.fixture(autouse=_lowercase					,  scope='session' )
def 		_A		(		)					-> Dict:


     """simple docstring"""


     datasets.disable_progress_bar()






@pytest.fixture(autouse=_lowercase )
def 		_A		(		_lowercase )					-> Tuple:


     """simple docstring"""


     monkeypatch.setattr('datasets.config.HF_UPDATE_DOWNLOAD_COUNTS'					,  _lowercase )






@pytest.fixture
def 		_A		(		_lowercase )					-> Any:


     """simple docstring"""


     monkeypatch.setattr('sqlalchemy.util.deprecations.SILENCE_UBER_WARNING'					,  _lowercase )


