from math import factorial
class     a_			:






 '''simple docstring'''






 def __init__(      self :  List[Any]      ,   lowercase__ :  List[str]      ,   lowercase__ :  str):







        '''simple docstring'''



        lowerCAmelCase__					     = real
        if isinstance(lowercase__      ,   lowercase__):
               lowerCAmelCase__					     = [1] * rank
        else:
               lowerCAmelCase__					     = rank




 def __repr__(      self :  int):







        '''simple docstring'''



        return (
            F"""{self.real}+"""
            F"""{'+'.join(str(lowercase__)+'E'+str(n+1)for n,dual in enumerate(self.duals))}"""
        )




 def 		__snake_case						(      self :  List[Any]):







        '''simple docstring'''



        lowerCAmelCase__					     = self.duals.copy()
        while cur[-1] == 0:
               cur.pop(-1)
        return Dual(self.real      ,   lowercase__)




 def __add__(      self :  Optional[Any]      ,   lowercase__ :  int):







        '''simple docstring'''



        if not isinstance(lowercase__      ,   lowercase__):
               return Dual(self.real + other      ,   self.duals)
        lowerCAmelCase__					     = self.duals.copy()
        lowerCAmelCase__					     = other.duals.copy()
        if len(lowercase__) > len(lowercase__):
               o_dual.extend([1] * (len(lowercase__) - len(lowercase__)))
        elif len(lowercase__) < len(lowercase__):
               s_dual.extend([1] * (len(lowercase__) - len(lowercase__)))
        lowerCAmelCase__					     = []
        for i in range(len(lowercase__)):
               new_duals.append(s_dual[i] + o_dual[i])
        return Dual(self.real + other.real      ,   lowercase__)

 UpperCAmelCase_     			= __add__




 def __sub__(      self :  str      ,   lowercase__ :  Union[str, Any]):







        '''simple docstring'''



        return self + other * -1




 def __mul__(      self :  List[Any]      ,   lowercase__ :  Union[str, Any]):







        '''simple docstring'''



        if not isinstance(lowercase__      ,   lowercase__):
               lowerCAmelCase__					     = []
               for i in self.duals:
                      new_duals.append(i * other)
               return Dual(self.real * other      ,   lowercase__)
        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      ,   lowercase__)

 UpperCAmelCase_     			= __mul__




 def __truediv__(      self :  List[Any]      ,   lowercase__ :  int):







        '''simple docstring'''



        if not isinstance(lowercase__      ,   lowercase__):
               lowerCAmelCase__					     = []
               for i in self.duals:
                      new_duals.append(i / other)
               return Dual(self.real / other      ,   lowercase__)
        raise ValueError




 def __floordiv__(      self :  Union[str, Any]      ,   lowercase__ :  int):







        '''simple docstring'''



        if not isinstance(lowercase__      ,   lowercase__):
               lowerCAmelCase__					     = []
               for i in self.duals:
                      new_duals.append(i // other)
               return Dual(self.real // other      ,   lowercase__)
        raise ValueError




 def __pow__(      self :  List[str]      ,   lowercase__ :  Tuple):







        '''simple docstring'''



        if n < 0 or isinstance(lowercase__      ,   lowercase__):
               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 				__lowerCamelCase		(						lowerCAmelCase__     ,  lowerCAmelCase__     ,  lowerCAmelCase__     ):
       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 				__lowerCamelCase		(						lowerCAmelCase__     ):
           return y**2 * y**4



    print(differentiate(f, 9, 2))

import argparse
from collections import defaultdict

import yaml


lowerCAmelCase__     						=			'docs/source/en/_toctree.yml'






def 				__lowerCamelCase		(						lowerCAmelCase__     ):
       lowerCAmelCase__					     = defaultdict(lowerCAmelCase__     )
       for doc in model_doc:
              counts[doc["local"]] += 1
       lowerCAmelCase__					     = [key for key, value in counts.items() if value > 1]

       lowerCAmelCase__					     = []
       for duplicate_key in duplicates:
              lowerCAmelCase__					     = list({doc['title'] for doc in model_doc if doc['local'] == duplicate_key}     )
              if len(lowerCAmelCase__     ) > 1:
                     raise ValueError(
                         F"""{duplicate_key} is present several times in the documentation table of content at """
                         '`docs/source/en/_toctree.yml` with different *Title* values. Choose one of those and remove the '
                         'others.'     )
              # Only add this once
              new_doc.append({'local': duplicate_key, 'title': titles[0]}     )

       # Add none duplicate-keys
       new_doc.extend([doc for doc in model_doc if counts[doc['local']] == 1]     )

       # Sort
       return sorted(lowerCAmelCase__     ,  key=lambda lowerCAmelCase__     : s["title"].lower()     )






def 				__lowerCamelCase		(						lowerCAmelCase__=False     ):
       with open(lowerCAmelCase__     ,  encoding='utf-8'     ) as f:
              lowerCAmelCase__					     = yaml.safe_load(f.read()     )

       # Get to the API doc
       lowerCAmelCase__					     = 0
       while content[api_idx]["title"] != "API":
              api_idx += 1
       lowerCAmelCase__					     = content[api_idx]['sections']

       # Then to the model doc
       lowerCAmelCase__					     = 0
       while api_doc[model_idx]["title"] != "Models":
              model_idx += 1

       lowerCAmelCase__					     = api_doc[model_idx]['sections']

       lowerCAmelCase__					     = [(idx, section) for idx, section in enumerate(lowerCAmelCase__     ) if 'sections' in section]
       lowerCAmelCase__					     = False
       for idx, modality_doc in modalities_docs:
              lowerCAmelCase__					     = modality_doc['sections']
              lowerCAmelCase__					     = clean_model_doc_toc(lowerCAmelCase__     )

              if old_modality_doc != new_modality_doc:
                     lowerCAmelCase__					     = True
                     if overwrite:
                            lowerCAmelCase__					     = new_modality_doc

       if diff:
              if overwrite:
                     lowerCAmelCase__					     = model_doc
                     lowerCAmelCase__					     = api_doc
                     with open(lowerCAmelCase__     ,  'w'     ,  encoding='utf-8'     ) as f:
                            f.write(yaml.dump(lowerCAmelCase__     ,  allow_unicode=lowerCAmelCase__     )     )
              else:
                     raise ValueError(
                         'The model doc part of the table of content is not properly sorted, run `make style` to fix this.'     )


if __name__ == "__main__":
    lowerCAmelCase__     						=			argparse.ArgumentParser()
    parser.add_argument('--fix_and_overwrite', action='store_true', help='Whether to fix inconsistencies.')
    lowerCAmelCase__     						=			parser.parse_args()

    check_model_doc(args.fix_and_overwrite)
