





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   (   _UpperCamelCase   ):

  """simple docstring"""


  a_      =			""""""
  a_      =			"""hf-legacy"""  # "hf://"" is reserved for hffs






  def __init__(    self			:		Optional[int] ,  lowerCAmelCase_			:		Optional[DatasetInfo] = None ,  lowerCAmelCase_			:		Optional[str] = None ,  **lowerCAmelCase_			:		Any ,  )							->						Tuple:
     super().__init__(self ,  **lowerCAmelCase_					)
     __lowerCAmelCase							     =     repo_info
     __lowerCAmelCase							     =     token
     __lowerCAmelCase							     =     None






  def     lowercase		(    self			:		Tuple					)							->						int:
     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(lowerCAmelCase_					): {'name': str(lowerCAmelCase_					), 'size': None, 'type': 'directory'}
                   for d in list(PurePosixPath(hf_file.rfilename					).parents					)[:-1]
               }					)






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






  def     lowercase		(    self			:		Dict ,  lowerCAmelCase_			:		Optional[Any] ,  **lowerCAmelCase_			:		Dict					)							->						Optional[Any]:
     self._get_dirs()
     __lowerCAmelCase							     =     self._strip_protocol(lowerCAmelCase_					)
     if path in self.dir_cache:
        return self.dir_cache[path]
     else:
        raise FileNotFoundError(lowerCAmelCase_					)






  def     lowercase		(    self			:		Any ,  lowerCAmelCase_			:		Union[str, Any] ,  lowerCAmelCase_			:		Tuple=False ,  **lowerCAmelCase_			:		Optional[int]					)							->						Tuple:
     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					)








from math import factorial



class     _UpperCAmelCase   :

  """simple docstring"""


  def __init__(    self			:		Dict ,  lowerCAmelCase_			:		Optional[int] ,  lowerCAmelCase_			:		str					)							->						Union[str, Any]:
     __lowerCAmelCase							     =     real
     if isinstance(lowerCAmelCase_ ,  lowerCAmelCase_					):
        __lowerCAmelCase							     =     [1] * rank
     else:
        __lowerCAmelCase							     =     rank






  def __repr__(    self			:		Optional[Any]					)							->						Tuple:
     return (
         f"""{self.real}+"""
         f"""{"+".join(str(lowerCAmelCase_					)+"E"+str(n+1					)for n,dual in enumerate(self.duals					)					)}"""
     )






  def     lowercase		(    self			:		str					)							->						Dict:
     __lowerCAmelCase							     =     self.duals.copy()
     while cur[-1] == 0:
        cur.pop(-1					)
     return Dual(self.real ,  lowerCAmelCase_					)






  def __add__(    self			:		Union[str, Any] ,  lowerCAmelCase_			:		Tuple					)							->						Optional[Any]:
     if not isinstance(lowerCAmelCase_ ,  lowerCAmelCase_					):
        return Dual(self.real + other ,  self.duals					)
     __lowerCAmelCase							     =     self.duals.copy()
     __lowerCAmelCase							     =     other.duals.copy()
     if len(lowerCAmelCase_					) > len(lowerCAmelCase_					):
        o_dual.extend([1] * (len(lowerCAmelCase_					) - len(lowerCAmelCase_					))					)
     elif len(lowerCAmelCase_					) < len(lowerCAmelCase_					):
        s_dual.extend([1] * (len(lowerCAmelCase_					) - len(lowerCAmelCase_					))					)
     __lowerCAmelCase							     =     []
     for i in range(len(lowerCAmelCase_					)					):
        new_duals.append(s_dual[i] + o_dual[i]					)
     return Dual(self.real + other.real ,  lowerCAmelCase_					)

  a_      =			__add__






  def __sub__(    self			:		int ,  lowerCAmelCase_			:		Dict					)							->						Optional[Any]:
     return self + other * -1






  def __mul__(    self			:		int ,  lowerCAmelCase_			:		Optional[int]					)							->						Dict:
     if not isinstance(lowerCAmelCase_ ,  lowerCAmelCase_					):
        __lowerCAmelCase							     =     []
        for i in self.duals:
           new_duals.append(i * other					)
        return Dual(self.real * other ,  lowerCAmelCase_					)
     __lowerCAmelCase							     =     [0] * (len(self.duals					) + len(other.duals					) + 1)
     for i, item in enumerate(self.duals					):
        for j, jtem in enumerate(other.duals					):
           new_duals[i + j + 1] += item * jtem
     for k in range(len(self.duals					)					):
        new_duals[k] += self.duals[k] * other.real
     for index in range(len(other.duals					)					):
        new_duals[index] += other.duals[index] * self.real
     return Dual(self.real * other.real ,  lowerCAmelCase_					)

  a_      =			__mul__






  def __truediv__(    self			:		Union[str, Any] ,  lowerCAmelCase_			:		str					)							->						Dict:
     if not isinstance(lowerCAmelCase_ ,  lowerCAmelCase_					):
        __lowerCAmelCase							     =     []
        for i in self.duals:
           new_duals.append(i / other					)
        return Dual(self.real / other ,  lowerCAmelCase_					)
     raise ValueError






  def __floordiv__(    self			:		str ,  lowerCAmelCase_			:		List[Any]					)							->						Union[str, Any]:
     if not isinstance(lowerCAmelCase_ ,  lowerCAmelCase_					):
        __lowerCAmelCase							     =     []
        for i in self.duals:
           new_duals.append(i // other					)
        return Dual(self.real // other ,  lowerCAmelCase_					)
     raise ValueError






  def __pow__(    self			:		Tuple ,  lowerCAmelCase_			:		Dict					)							->						List[str]:
     if n < 0 or isinstance(lowerCAmelCase_ ,  lowerCAmelCase_					):
        raise ValueError('power must be a positive integer'					)
     if n == 0:
        return 1
     if n == 1:
        return self
     __lowerCAmelCase							     =     self
     for _ in range(n - 1					):
        x *= self
     return x





def   a_   (			lowerCAmelCase_				:      List[str],     lowerCAmelCase_				:      Optional[Any],     lowerCAmelCase_				:      Optional[Any]     ):
   if not callable(lowerCAmelCase_     ):
      raise ValueError('differentiate() requires a function as input for func'     )
   if not isinstance(lowerCAmelCase_,     (float, int)     ):
      raise ValueError('differentiate() requires a float as input for position'     )
   if not isinstance(lowerCAmelCase_,     lowerCAmelCase_     ):
      raise ValueError('differentiate() requires an int as input for order'     )
   __lowerCAmelCase							     =     Dual(lowerCAmelCase_,     1     )
   __lowerCAmelCase							     =     func(lowerCAmelCase_     )
   if order == 0:
      return result.real
   return result.duals[order - 1] * factorial(lowerCAmelCase_     )


if __name__ == "__main__":
     import doctest

     doctest.testmod()

     def   a_   (			lowerCAmelCase_				:      int     ):
        return y**2 * y**4




     print(differentiate(f, 9, 2))

