






'''simple docstring'''
from pathlib import PurePosixPath
from typing import Optional

import fsspec
from fsspec import AbstractFileSystem
from huggingface_hub.hf_api import DatasetInfo

from ..utils.file_utils import get_authentication_headers_for_url
from ..utils.hub import hf_hub_url






class      __SCREAMING_SNAKE_CASE      (			lowerCamelCase				):
 snake_case_  							=							""""""
 snake_case_  							=							"""hf-legacy"""  # "hf://"" is reserved for hffs




 def __init__(      self	:							Union[str, Any]					,      __lowercase	:							Optional[DatasetInfo] = None					,      __lowercase	:							Optional[str] = None					,      **__lowercase	:							Dict					,      )	->						List[Any]:
       super().__init__(self					,      **__UpperCamelCase      )
       SCREAMING_SNAKE_CASE__     :				List[Any]									=repo_info
       SCREAMING_SNAKE_CASE__     :				Any									=token
       SCREAMING_SNAKE_CASE__     :				int									=None




 def      __magic_name__	(      self	:							Optional[int]      )	->						Optional[int]:
       if self.dir_cache is None:
             SCREAMING_SNAKE_CASE__     :				List[str]									={}
             for hf_file in self.repo_info.siblings:
                   # TODO(QL): add sizes
                   SCREAMING_SNAKE_CASE__     :				Union[str, Any]									={
                       '''name''': hf_file.rfilename,
                       '''size''': None,
                       '''type''': '''file''',
                   }
                   self.dir_cache.update(
                       {
                           str(__UpperCamelCase      ): {'''name''': str(__UpperCamelCase      ), '''size''': None, '''type''': '''directory'''}
                           for d in list(PurePosixPath(hf_file.rfilename      ).parents      )[:-1]
                       }      )




 def      __magic_name__	(      self	:							Any					,      __lowercase	:							str					,      __lowercase	:							str = "rb"					,      **__lowercase	:							Dict					,      )	->						Any:
       if not isinstance(self.repo_info					,      __UpperCamelCase      ):
             raise NotImplementedError(F"Open is only implemented for dataset repositories, but got {self.repo_info}"      )
       SCREAMING_SNAKE_CASE__     :				Dict									=hf_hub_url(self.repo_info.id					,      __UpperCamelCase					,      revision=self.repo_info.sha      )
       return fsspec.open(
           __UpperCamelCase					,      mode=__UpperCamelCase					,      headers=get_authentication_headers_for_url(__UpperCamelCase					,      use_auth_token=self.token      )					,      client_kwargs={'''trust_env''': True}					,      ).open()




 def      __magic_name__	(      self	:							List[str]					,      __lowercase	:							List[str]					,      **__lowercase	:							Dict      )	->						int:
       self._get_dirs()
       SCREAMING_SNAKE_CASE__     :				Union[str, Any]									=self._strip_protocol(__UpperCamelCase      )
       if path in self.dir_cache:
             return self.dir_cache[path]
       else:
             raise FileNotFoundError(__UpperCamelCase      )




 def      __magic_name__	(      self	:							str					,      __lowercase	:							Optional[Any]					,      __lowercase	:							Union[str, Any]=False					,      **__lowercase	:							Any      )	->						Any:
       self._get_dirs()
       SCREAMING_SNAKE_CASE__     :				List[Any]									=PurePosixPath(path.strip('''/'''      )      )
       SCREAMING_SNAKE_CASE__     :				Any									={}
       for p, f in self.dir_cache.items():
             SCREAMING_SNAKE_CASE__     :				Any									=PurePosixPath(p.strip('''/'''      )      )
             SCREAMING_SNAKE_CASE__     :				Any									=p.parent
             if root == path:
                   SCREAMING_SNAKE_CASE__     :				List[Any]									=f
       SCREAMING_SNAKE_CASE__     :				Dict									=list(paths.values()      )
       if detail:
             return out
       else:
             return sorted(f['''name'''] for f in out      )







'''simple docstring'''
from __future__ import annotations

from collections.abc import Callable

a_					= list[list[float | int]]





def  _a(  UpperCamelCase__				:						Matrix,	UpperCamelCase__				:						Matrix							):




      '''simple docstring'''






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

      for row in range(UpperCamelCase__							):
            for col in range(UpperCamelCase__							):
                  SCREAMING_SNAKE_CASE__     :				Tuple									=matrix[row][col]

            SCREAMING_SNAKE_CASE__     :				Optional[int]									=vector[row][0]

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

            for rowa in range(row + 1,	UpperCamelCase__							):
                  SCREAMING_SNAKE_CASE__     :				Union[str, Any]									=augmented[rowa][col] / augmented[row][col]
                  SCREAMING_SNAKE_CASE__     :				Tuple									=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__							):
                  SCREAMING_SNAKE_CASE__     :				Optional[Any]									=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],	1_0							)] for row in range(UpperCamelCase__							)
      ]





def  _a(  UpperCamelCase__				:						list[int]							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__     :				int									=len(UpperCamelCase__							)
      SCREAMING_SNAKE_CASE__     :				Matrix									=[[0 for _ in range(UpperCamelCase__							)] for _ in range(UpperCamelCase__							)]
      SCREAMING_SNAKE_CASE__     :				Matrix									=[[0] for _ in range(UpperCamelCase__							)]
      SCREAMING_SNAKE_CASE__     :				Matrix
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int

      for x_val, y_val in enumerate(UpperCamelCase__							):
            for col in range(UpperCamelCase__							):
                  SCREAMING_SNAKE_CASE__     :				Optional[int]									=(x_val + 1) ** (size - col - 1)
            SCREAMING_SNAKE_CASE__     :				Dict									=y_val

      SCREAMING_SNAKE_CASE__     :				Optional[int]									=solve(UpperCamelCase__,	UpperCamelCase__							)

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

      return interpolated_func





def  _a(  UpperCamelCase__				:						int							):




      '''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  _a(  UpperCamelCase__				:						Callable[[int], int] = question_function,	UpperCamelCase__				:						int = 1_0							):




      '''simple docstring'''






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

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

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

      for poly in polynomials:
            SCREAMING_SNAKE_CASE__     :				Any									=1
            while func(UpperCamelCase__							) == poly(UpperCamelCase__							):
                  x_val += 1

            ret += poly(UpperCamelCase__							)

      return ret


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