





from math import factorial







class   __lowerCAmelCase			:





   def __init__( self					,			snake_case					,			snake_case      )				->  Tuple:
      """simple docstring"""





      a__	:						str      		=  real
      if isinstance(snake_case					,			snake_case      ):
         a__	:						int      		=  [1] * rank
      else:
         a__	:						Any      		=  rank





   def __repr__( self      )				->  Union[str, Any]:
      """simple docstring"""





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





   def 	_snake_case ( self      )				->  Union[str, Any]:
      """simple docstring"""





      a__	:						List[Any]      		=  self.duals.copy()
      while cur[-1] == 0:
         cur.pop(-1      )
      return Dual(self.real					,			snake_case      )





   def __add__( self					,			snake_case      )				->  Optional[int]:
      """simple docstring"""





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

   _UpperCamelCase :						List[str]     		=				__add__





   def __sub__( self					,			snake_case      )				->  Optional[int]:
      """simple docstring"""





      return self + other * -1





   def __mul__( self					,			snake_case      )				->  Optional[Any]:
      """simple docstring"""





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

   _UpperCamelCase :						List[Any]     		=				__mul__





   def __truediv__( self					,			snake_case      )				->  Tuple:
      """simple docstring"""





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





   def __floordiv__( self					,			snake_case      )				->  Union[str, Any]:
      """simple docstring"""





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





   def __pow__( self					,			snake_case      )				->  Any:
      """simple docstring"""





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







def       _A  (      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"   )
   a__	:						Tuple      		=  Dual(lowerCamelCase							, 1   )
   a__	:						Any      		=  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   ):
     return y**2 * y**4


  print(differentiate(f, 9, 2))








import json
from typing import List, Optional, Tuple

from tokenizers import normalizers

from ...tokenization_utils_fast import PreTrainedTokenizerFast
from .tokenization_lxmert import LxmertTokenizer


SCREAMING_SNAKE_CASE__       :			Optional[Any]			      =						{"""vocab_file""": """vocab.txt""", """tokenizer_file""": """tokenizer.json"""}

SCREAMING_SNAKE_CASE__       :			List[Any]			      =						{
    """vocab_file""": {
        """unc-nlp/lxmert-base-uncased""": """https://huggingface.co/unc-nlp/lxmert-base-uncased/resolve/main/vocab.txt""",
    },
    """tokenizer_file""": {
        """unc-nlp/lxmert-base-uncased""": (
            """https://huggingface.co/unc-nlp/lxmert-base-uncased/resolve/main/tokenizer.json"""
        ),
    },
}

SCREAMING_SNAKE_CASE__       :			Any			      =						{
    """unc-nlp/lxmert-base-uncased""": 5_1_2,
}

SCREAMING_SNAKE_CASE__       :			Optional[int]			      =						{
    """unc-nlp/lxmert-base-uncased""": {"""do_lower_case""": True},
}







class   __lowerCAmelCase			(					_UpperCamelCase  ):
   _UpperCamelCase :						List[str]     		=				VOCAB_FILES_NAMES
   _UpperCamelCase :						str     		=				PRETRAINED_VOCAB_FILES_MAP
   _UpperCamelCase :						List[str]     		=				PRETRAINED_INIT_CONFIGURATION
   _UpperCamelCase :						Optional[int]     		=				PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
   _UpperCamelCase :						Optional[Any]     		=				LxmertTokenizer





   def __init__( self					,			snake_case=None					,			snake_case=None					,			snake_case=True					,			snake_case="[UNK]"					,			snake_case="[SEP]"					,			snake_case="[PAD]"					,			snake_case="[CLS]"					,			snake_case="[MASK]"					,			snake_case=True					,			snake_case=None					,			**snake_case					,			)				->  Any:
      """simple docstring"""





      super().__init__(
          snake_case					,			tokenizer_file=snake_case					,			do_lower_case=snake_case					,			unk_token=snake_case					,			sep_token=snake_case					,			pad_token=snake_case					,			cls_token=snake_case					,			mask_token=snake_case					,			tokenize_chinese_chars=snake_case					,			strip_accents=snake_case					,			**snake_case					,			)

      a__	:						Optional[Any]      		=  json.loads(self.backend_tokenizer.normalizer.__getstate__()      )
      if (
          normalizer_state.get("lowercase"					,			snake_case      ) != do_lower_case
          or normalizer_state.get("strip_accents"					,			snake_case      ) != strip_accents
          or normalizer_state.get("handle_chinese_chars"					,			snake_case      ) != tokenize_chinese_chars
      ):
         a__	:						str      		=  getattr(snake_case					,			normalizer_state.pop("type"      )      )
         a__	:						Tuple      		=  do_lower_case
         a__	:						Union[str, Any]      		=  strip_accents
         a__	:						str      		=  tokenize_chinese_chars
         a__	:						List[str]      		=  normalizer_class(**snake_case      )

      a__	:						str      		=  do_lower_case





   def 	_snake_case ( self					,			snake_case					,			snake_case=None      )				->  List[str]:
      """simple docstring"""





      a__	:						Optional[int]      		=  [self.cls_token_id] + token_ids_a + [self.sep_token_id]

      if token_ids_a:
         output += token_ids_a + [self.sep_token_id]

      return output





   def 	_snake_case ( self					,			snake_case					,			snake_case = None      )				->  List[int]:
      """simple docstring"""





      a__	:						Tuple      		=  [self.sep_token_id]
      a__	:						str      		=  [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      ) * [0] + len(token_ids_a + sep      ) * [1]





   def 	_snake_case ( self					,			snake_case					,			snake_case = None      )				->  Tuple[str]:
      """simple docstring"""





      a__	:						Optional[int]      		=  self._tokenizer.model.save(snake_case					,			name=snake_case      )
      return tuple(snake_case      )

