


from __future__ import annotations

from collections.abc import Callable

_SCREAMING_SNAKE_CASE      :			Tuple      				=   list[list[float | int]]
def       UpperCAmelCase__						(UpperCamelCase_							,UpperCamelCase_    ):



     """simple docstring"""






     snake_case					=    len(UpperCamelCase_    )
     snake_case					=    [[0 for _ in range(size + 1    )] for _ in range(UpperCamelCase_    )]
     snake_case					=    42
     snake_case					=    42
     snake_case					=    42
     snake_case					=    42
     snake_case					=    42
     snake_case					=    42

     for row in range(UpperCamelCase_    ):
          for col in range(UpperCamelCase_    ):
               snake_case					=    matrix[row][col]

          snake_case					=    vector[row][0]

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

          for rowa in range(row + 1							,UpperCamelCase_    ):
               snake_case					=    augmented[rowa][col] / augmented[row][col]
               snake_case					=    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							,UpperCamelCase_    ):
          for row in range(UpperCamelCase_    ):
               snake_case					=    augmented[row][col] / augmented[col][col]
               for cola in range(UpperCamelCase_							,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(UpperCamelCase_    )
     ]
def       UpperCAmelCase__						(UpperCamelCase_    ):



     """simple docstring"""






     snake_case					=    len(UpperCamelCase_    )
     snake_case					=    [[0 for _ in range(UpperCamelCase_    )] for _ in range(UpperCamelCase_    )]
     snake_case					=    [[0] for _ in range(UpperCamelCase_    )]
     snake_case					=    42
     snake_case					=    42
     snake_case					=    42
     snake_case					=    42

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

     snake_case					=    solve(UpperCamelCase_							,UpperCamelCase_    )

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

     return interpolated_func
def       UpperCAmelCase__						(UpperCamelCase_    ):



     """simple docstring"""






     return (
         1
         - variable
         + variable**2
         - variable**3
         + variable**4
         - variable**5
         + variable**6
         - variable**7
         + variable**8
         - variable**9
         + variable**10
     )
def       UpperCAmelCase__						(UpperCamelCase_ = question_function							,UpperCamelCase_ = 10    ):



     """simple docstring"""






     snake_case					=    [func(UpperCamelCase_    ) for x_val in range(1							,order + 1    )]

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

     snake_case					=    0
     snake_case					=    42
     snake_case					=    42

     for poly in polynomials:
          snake_case					=    1
          while func(UpperCamelCase_    ) == poly(UpperCamelCase_    ):
               x_val += 1

          ret += poly(UpperCamelCase_    )

     return ret


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








# tests directory-specific settings - this file is run automatically
# by pytest before any tests are run

import sys
import warnings
from os.path import abspath, dirname, join


# allow having multiple repository checkouts and not needing to remember to rerun
# 'pip install -e .[dev]' when switching between checkouts and running tests.
_SCREAMING_SNAKE_CASE      :			Union[str, Any]      				=   abspath(join(dirname(dirname(dirname(__file__))), "src"))
sys.path.insert(1, git_repo_path)


# silence FutureWarning warnings in tests since often we can't act on them until
# they become normal warnings - i.e. the tests still need to test the current functionality
warnings.simplefilter(action="ignore", category=FutureWarning)
def       UpperCAmelCase__						(UpperCamelCase_    ):



     """simple docstring"""






     from transformers.testing_utils import pytest_addoption_shared

     pytest_addoption_shared(UpperCamelCase_    )

def       UpperCAmelCase__						(UpperCamelCase_    ):



     """simple docstring"""






     from transformers.testing_utils import pytest_terminal_summary_main

     snake_case					=    terminalreporter.config.getoption('''--make-reports'''    )
     if make_reports:
          pytest_terminal_summary_main(UpperCamelCase_							,id=UpperCamelCase_    )




