



from __future__ import annotations

from collections.abc import Callable

lowerCAmelCase__						:	Any					=list[list[float | int]]






def       __lowercase  (					a__				,  a__  )							->					Union[str, Any]:
							__SCREAMING_SNAKE_CASE										=   len(_UpperCamelCase  )
							__SCREAMING_SNAKE_CASE										=   [[0 for _ in range(size + 1  )] for _ in range(_UpperCamelCase  )]
							__SCREAMING_SNAKE_CASE										=   42
							__SCREAMING_SNAKE_CASE										=   42
							__SCREAMING_SNAKE_CASE										=   42
							__SCREAMING_SNAKE_CASE										=   42
							__SCREAMING_SNAKE_CASE										=   42
							__SCREAMING_SNAKE_CASE										=   42

							for row in range(_UpperCamelCase  ):
														for col in range(_UpperCamelCase  ):
																					__SCREAMING_SNAKE_CASE										=   matrix[row][col]

														__SCREAMING_SNAKE_CASE										=   vector[row][0]

							__SCREAMING_SNAKE_CASE										=   0
							__SCREAMING_SNAKE_CASE										=   0
							while row < size and col < size:
														# pivoting
														__SCREAMING_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:
																					__SCREAMING_SNAKE_CASE				,			__SCREAMING_SNAKE_CASE										=   augmented[pivot_row], augmented[row]

														for rowa in range(row + 1				,  _UpperCamelCase  ):
																					__SCREAMING_SNAKE_CASE										=   augmented[rowa][col] / augmented[row][col]
																					__SCREAMING_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  ):
																					__SCREAMING_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       __lowercase  (					a__  )							->					Optional[int]:
							__SCREAMING_SNAKE_CASE										=   len(_UpperCamelCase  )
							__SCREAMING_SNAKE_CASE										=   [[0 for _ in range(_UpperCamelCase  )] for _ in range(_UpperCamelCase  )]
							__SCREAMING_SNAKE_CASE										=   [[0] for _ in range(_UpperCamelCase  )]
							__SCREAMING_SNAKE_CASE										=   42
							__SCREAMING_SNAKE_CASE										=   42
							__SCREAMING_SNAKE_CASE										=   42
							__SCREAMING_SNAKE_CASE										=   42

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

							__SCREAMING_SNAKE_CASE										=   solve(_UpperCamelCase				,  _UpperCamelCase  )

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

							return interpolated_func






def       __lowercase  (					a__  )							->					Optional[Any]:
							return (
							    1
							    - variable
							    + variable**2
							    - variable**3
							    + variable**4
							    - variable**5
							    + variable**6
							    - variable**7
							    + variable**8
							    - variable**9
							    + variable**10
							)






def       __lowercase  (					a__ = question_function				,  a__ = 10  )							->					Dict:
							__SCREAMING_SNAKE_CASE										=   [func(_UpperCamelCase  ) for x_val in range(1				,  order + 1  )]

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

							__SCREAMING_SNAKE_CASE										=   0
							__SCREAMING_SNAKE_CASE										=   42
							__SCREAMING_SNAKE_CASE										=   42

							for poly in polynomials:
														__SCREAMING_SNAKE_CASE										=   1
														while func(_UpperCamelCase  ) == poly(_UpperCamelCase  ):
																					x_val += 1

														ret += poly(_UpperCamelCase  )

							return ret


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










"""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     _UpperCamelCase    (  lowerCAmelCase__						):
							'''simple docstring'''







							__UpperCAmelCase		:       Union[str, Any]							 =""""""
							__UpperCAmelCase		:       Optional[int]							 ="""hf-legacy"""  # "hf://"" is reserved for hffs

							def __init__(	self       ,  __a = None       ,  __a = None       ,  **__a       ,  ):
										super().__init__(self       ,  **__a      )
										__lowerCAmelCase							       =     repo_info
										__lowerCAmelCase							       =     token
										__lowerCAmelCase							       =     None

							def      snake_case							(	self      ):
										if self.dir_cache is None:
													__lowerCAmelCase							       =     {}
													for hf_file in self.repo_info.siblings:
																# TODO(QL): add sizes
																__lowerCAmelCase							       =     {
																    "name": hf_file.rfilename,
																    "size": None,
																    "type": "file",
																}
																self.dir_cache.update(
																    {
																        str(__a      ): {"name": str(__a      ), "size": None, "type": "directory"}
																        for d in list(PurePosixPath(hf_file.rfilename      ).parents      )[:-1]
																    }      )

							def      snake_case							(	self       ,  __a       ,  __a = "rb"       ,  **__a       ,  ):
										if not isinstance(self.repo_info       ,  __a      ):
													raise NotImplementedError(f"Open is only implemented for dataset repositories, but got {self.repo_info}"      )
										__lowerCAmelCase							       =     hf_hub_url(self.repo_info.id       ,  __a       ,  revision=self.repo_info.sha      )
										return fsspec.open(
										    __a       ,  mode=__a       ,  headers=get_authentication_headers_for_url(__a       ,  use_auth_token=self.token      )       ,  client_kwargs={"trust_env": True}       ,  ).open()

							def      snake_case							(	self       ,  __a       ,  **__a      ):
										self._get_dirs()
										__lowerCAmelCase							       =     self._strip_protocol(__a      )
										if path in self.dir_cache:
													return self.dir_cache[path]
										else:
													raise FileNotFoundError(__a      )



							def      snake_case							(	self       ,  __a       ,  __a=False       ,  **__a      ):
										self._get_dirs()
										__lowerCAmelCase							       =     PurePosixPath(path.strip("/"      )      )
										__lowerCAmelCase							       =     {}
										for p, f in self.dir_cache.items():
													__lowerCAmelCase							       =     PurePosixPath(p.strip("/"      )      )
													__lowerCAmelCase							       =     p.parent
													if root == path:
																__lowerCAmelCase							       =     f
										__lowerCAmelCase							       =     list(paths.values()      )
										if detail:
													return out
										else:
													return sorted(f["name"] for f in out      )




