"""simple docstring"""




from math import factorial
class 						__A							:






     def __init__(		self				,     a__				,     a__  ):
       _lowerCAmelCase						:       Dict  			=     real
       if isinstance(a__				,     a__  ):
         _lowerCAmelCase						:       int  			=     [1] * rank
       else:
         _lowerCAmelCase						:       int  			=     rank






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






     def     __A  (		self  ):
       _lowerCAmelCase						:       str  			=     self.duals.copy()
       while cur[-1] == 0:
         cur.pop(-1  )
       return Dual(self.real				,     a__  )






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

     _UpperCamelCase							:			Optional[Any]							=		__add__






     def __sub__(		self				,     a__  ):
       return self + other * -1






     def __mul__(		self				,     a__  ):
       if not isinstance(a__				,     a__  ):
         _lowerCAmelCase						:       Any  			=     []
         for i in self.duals:
           new_duals.append(i * other  )
         return Dual(self.real * other				,     a__  )
       _lowerCAmelCase						:       Union[str, Any]  			=     [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				,     a__  )

     _UpperCamelCase							:			Optional[Any]							=		__mul__






     def __truediv__(		self				,     a__  ):
       if not isinstance(a__				,     a__  ):
         _lowerCAmelCase						:       Tuple  			=     []
         for i in self.duals:
           new_duals.append(i / other  )
         return Dual(self.real / other				,     a__  )
       raise ValueError






     def __floordiv__(		self				,     a__  ):
       if not isinstance(a__				,     a__  ):
         _lowerCAmelCase						:       List[str]  			=     []
         for i in self.duals:
           new_duals.append(i // other  )
         return Dual(self.real // other				,     a__  )
       raise ValueError






     def __pow__(		self				,     a__  ):
       if n < 0 or isinstance(a__				,     a__  ):
         raise ValueError("""power must be a positive integer"""  )
       if n == 0:
         return 1
       if n == 1:
         return self
       _lowerCAmelCase						:       Union[str, Any]  			=     self
       for _ in range(n - 1  ):
         x *= self
       return x







def 							SCREAMING_SNAKE_CASE     (			_lowerCamelCase						:       Union[str, Any]			,_lowerCamelCase						:       int			,_lowerCamelCase						:       List[str]	)       ->      Tuple:
  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						:       int  			=     Dual(_lowerCamelCase			,1	)
  _lowerCAmelCase						:       str  			=     func(_lowerCamelCase	)
  if order == 0:
    return result.real
  return result.duals[order - 1] * factorial(_lowerCamelCase	)


if __name__ == "__main__":
     import doctest

     doctest.testmod()





     def 							SCREAMING_SNAKE_CASE     (			_lowerCamelCase						:       Dict	)       ->      Dict:
       return y**2 * y**4






     print(differentiate(f, 9, 2))








'''simple docstring'''




from typing import List, Optional

from tokenizers import ByteLevelBPETokenizer

from ...tokenization_utils_fast import PreTrainedTokenizerFast
from ...utils import logging
from .tokenization_blenderbot_small import BlenderbotSmallTokenizer


__snake_case    						=logging.get_logger(__name__)

__snake_case    						={
    """vocab_file""": """vocab.json""",
    """merges_file""": """merges.txt""",
    """tokenizer_config_file""": """tokenizer_config.json""",
}

__snake_case    						={
    """vocab_file""": {
        """facebook/blenderbot_small-90M""": """https://huggingface.co/facebook/blenderbot_small-90M/resolve/main/vocab.json"""
    },
    """merges_file""": {
        """facebook/blenderbot_small-90M""": """https://huggingface.co/facebook/blenderbot_small-90M/resolve/main/merges.txt"""
    },
    """tokenizer_config_file""": {
        """facebook/blenderbot_small-90M""": (
            """https://huggingface.co/facebook/blenderbot_small-90M/resolve/main/tokenizer_config.json"""
        )
    },
}

__snake_case    						={
    """facebook/blenderbot_small-90M""": 512,
}

class 		UpperCAmelCase_      (  __lowercase		):
     lowerCamelCase				:	Tuple		=     VOCAB_FILES_NAMES
     lowerCamelCase				:	Optional[int]		=     PRETRAINED_VOCAB_FILES_MAP
     lowerCamelCase				:	Union[str, Any]		=     PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
     lowerCamelCase				:	Optional[Any]		=     BlenderbotSmallTokenizer





     def __init__( self       :      Any    ,      UpperCAmelCase__       :      Union[str, Any]=None    ,      UpperCAmelCase__       :      Dict=None    ,      UpperCAmelCase__       :      int="<|endoftext|>"    ,      UpperCAmelCase__       :      Dict="<|endoftext|>"    ,      UpperCAmelCase__       :      str="<|endoftext|>"    ,      UpperCAmelCase__       :      str=False    ,      UpperCAmelCase__       :      Tuple=True    ,      **UpperCAmelCase__       :      Optional[Any]    ,      )				->  Any:
        super().__init__(
            ByteLevelBPETokenizer(
                vocab=UpperCAmelCase__    ,      merges=UpperCAmelCase__    ,      add_prefix_space=UpperCAmelCase__    ,      trim_offsets=UpperCAmelCase__    ,      )    ,      bos_token=UpperCAmelCase__    ,      eos_token=UpperCAmelCase__    ,      unk_token=UpperCAmelCase__    ,      **UpperCAmelCase__    ,      )
        lowerCAmelCase     =			add_prefix_space





     def 							__UpperCAmelCase      ( self       :      List[Any]    ,      UpperCAmelCase__       :      Union[str, Any]    ,      UpperCAmelCase__       :      Dict=None    )				->  Any:
        lowerCAmelCase     =			[self.bos_token_id] + token_ids_a + [self.eos_token_id]
        if token_ids_a is None:
           return output

        return output + [self.eos_token_id] + token_ids_a + [self.eos_token_id]





     def 							__UpperCAmelCase      ( self       :      Any    ,      UpperCAmelCase__       :      List[int]    ,      UpperCAmelCase__       :      Optional[List[int]] = None    )				->  List[int]:
        lowerCAmelCase     =			[self.sep_token_id]
        lowerCAmelCase     =			[self.cls_token_id]

        if token_ids_a is None:
           return len(cls + token_ids_a + sep    ) * [0]
        return len(cls + token_ids_a + sep + sep + token_ids_a + sep    ) * [0]





