


'''simple docstring'''







from __future__ import annotations

from collections.abc import Callable

lowerCAmelCase    :     Optional[int]					=						list[list[float | int]]






def 			lowercase				(_A   ,						_A					):







       """simple docstring"""







       _lowerCAmelCase    :							int   			=       len(_A					)
       _lowerCAmelCase    :							Matrix   			=       [[0 for _ in range(size + 1					)] for _ in range(_A					)]
       _lowerCAmelCase    :							int
       _lowerCAmelCase    :							int
       _lowerCAmelCase    :							int
       _lowerCAmelCase    :							int
       _lowerCAmelCase    :							int
       _lowerCAmelCase    :							float

       for row in range(_A					):
              for col in range(_A					):
                     _lowerCAmelCase    :							List[str]   			=       matrix[row][col]

              _lowerCAmelCase    :							List[Any]   			=       vector[row][0]

       _lowerCAmelCase    :							Optional[Any]   			=       0
       _lowerCAmelCase    :							List[str]   			=       0
       while row < size and col < size:
              # pivoting
              _lowerCAmelCase    :							str   			=       max((abs(augmented[rowa][col]					), rowa) for rowa in range(_A   ,						_A					)					)[
                  1
              ]
              if augmented[pivot_row][col] == 0:
                     col += 1
                     continue
              else:
                     _lowerCAmelCase			,     _lowerCAmelCase    :							Tuple   			=       augmented[pivot_row], augmented[row]

              for rowa in range(row + 1   ,						_A					):
                     _lowerCAmelCase    :							Union[str, Any]   			=       augmented[rowa][col] / augmented[row][col]
                     _lowerCAmelCase    :							List[str]   			=       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   ,						_A					):
              for row in range(_A					):
                     _lowerCAmelCase    :							Union[str, Any]   			=       augmented[row][col] / augmented[col][col]
                     for cola in range(_A   ,						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]   ,						1_0					)] for row in range(_A					)
       ]






def 			lowercase				(_A					):







       """simple docstring"""







       _lowerCAmelCase    :							int   			=       len(_A					)
       _lowerCAmelCase    :							Matrix   			=       [[0 for _ in range(_A					)] for _ in range(_A					)]
       _lowerCAmelCase    :							Matrix   			=       [[0] for _ in range(_A					)]
       _lowerCAmelCase    :							Matrix
       _lowerCAmelCase    :							int
       _lowerCAmelCase    :							int
       _lowerCAmelCase    :							int

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

       _lowerCAmelCase    :							Optional[int]   			=       solve(_A   ,						_A					)

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

       return interpolated_func






def 			lowercase				(_A					):







       """simple docstring"""







       return (
           1
           - variable
           + variable**2
           - variable**3
           + variable**4
           - variable**5
           + variable**6
           - variable**7
           + variable**8
           - variable**9
           + variable**1_0
       )






def 			lowercase				(_A = question_function   ,						_A = 1_0					):







       """simple docstring"""







       _lowerCAmelCase    :							list[int]   			=       [func(_A					) for x_val in range(1   ,						order + 1					)]

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

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

       for poly in polynomials:
              _lowerCAmelCase    :							Union[str, Any]   			=       1
              while func(_A					) == poly(_A					):
                     x_val += 1

              ret += poly(_A					)

       return ret


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





'''simple docstring'''







from typing import TYPE_CHECKING

from ....utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


lowerCAmelCase    :     Optional[int]					=						{
    """configuration_mctct""": ["""MCTCT_PRETRAINED_CONFIG_ARCHIVE_MAP""", """MCTCTConfig"""],
    """feature_extraction_mctct""": ["""MCTCTFeatureExtractor"""],
    """processing_mctct""": ["""MCTCTProcessor"""],
}


try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       lowerCAmelCase    :     List[str]					=						[
           """MCTCT_PRETRAINED_MODEL_ARCHIVE_LIST""",
           """MCTCTForCTC""",
           """MCTCTModel""",
           """MCTCTPreTrainedModel""",
       ]


if TYPE_CHECKING:
       from .configuration_mctct import MCTCT_PRETRAINED_CONFIG_ARCHIVE_MAP, MCTCTConfig
       from .feature_extraction_mctct import MCTCTFeatureExtractor
       from .processing_mctct import MCTCTProcessor

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_mctct import MCTCT_PRETRAINED_MODEL_ARCHIVE_LIST, MCTCTForCTC, MCTCTModel, MCTCTPreTrainedModel

else:
       import sys

       lowerCAmelCase    :     Tuple					=						_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)

