

'''simple docstring'''
from math import factorial


class        a__  :


   def __init__(			self      ,    _UpperCamelCase      ,    _UpperCamelCase  ):





      """simple docstring"""





      _lowercase      :				Dict      					=       real
      if isinstance(snake_case__      ,    snake_case__  ):
         _lowercase      :				str      					=       [1] * rank
      else:
         _lowercase      :				List[Any]      					=       rank


   def __repr__(			self  ):





      """simple docstring"""





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


   def 						_lowerCamelCase       (			self  ):





      """simple docstring"""





      _lowercase      :				List[str]      					=       self.duals.copy()
      while cur[-1] == 0:
         cur.pop(-1  )
      return Dual(self.real      ,    snake_case__  )


   def __add__(			self      ,    _UpperCamelCase  ):





      """simple docstring"""





      if not isinstance(snake_case__      ,    snake_case__  ):
         return Dual(self.real + other      ,    self.duals  )
      _lowercase      :				List[str]      					=       self.duals.copy()
      _lowercase      :				Optional[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__  ))  )
      _lowercase      :				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__  )

   _SCREAMING_SNAKE_CASE   :					Union[str, Any]     	=							__add__


   def __sub__(			self      ,    _UpperCamelCase  ):





      """simple docstring"""





      return self + other * -1


   def __mul__(			self      ,    _UpperCamelCase  ):





      """simple docstring"""





      if not isinstance(snake_case__      ,    snake_case__  ):
         _lowercase      :				Dict      					=       []
         for i in self.duals:
            new_duals.append(i * other  )
         return Dual(self.real * other      ,    snake_case__  )
      _lowercase      :				int      					=       [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__  )

   _SCREAMING_SNAKE_CASE   :					Optional[Any]     	=							__mul__


   def __truediv__(			self      ,    _UpperCamelCase  ):





      """simple docstring"""





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


   def __floordiv__(			self      ,    _UpperCamelCase  ):





      """simple docstring"""





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






   def __pow__(			self      ,    _UpperCamelCase  ):





      """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
      _lowercase      :				Tuple      					=       self
      for _ in range(n - 1  ):
         x *= self
      return x







def  _A		(     snake_case		,							snake_case		,							snake_case					)      ->     str:







   if not callable(_A					):
      raise ValueError("differentiate() requires a function as input for func"					)
   if not isinstance(_A		,							(float, int)					):
      raise ValueError("differentiate() requires a float as input for position"					)
   if not isinstance(_A		,							_A					):
      raise ValueError("differentiate() requires an int as input for order"					)
   _lowercase      :				str      					=       Dual(_A		,							1					)
   _lowercase      :				int      					=       func(_A					)
   if order == 0:
      return result.real
   return result.duals[order - 1] * factorial(_A					)


if __name__ == "__main__":
    import doctest

    doctest.testmod()







    def  _A		(     snake_case					)      ->     Union[str, Any]:
       return y**2 * y**4

    print(differentiate(f, 9, 2))









'''simple docstring'''
import os
from typing import List, Optional, Union

from ...image_processing_utils import BatchFeature
from ...image_utils import ImageInput
from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import PaddingStrategy, PreTokenizedInput, TextInput, TruncationStrategy
from ...utils import TensorType
from ..auto import AutoTokenizer


class        a__  (							lowerCamelCase_  ):
   _SCREAMING_SNAKE_CASE   :					Any     	=							['image_processor', 'tokenizer']
   _SCREAMING_SNAKE_CASE   :					Dict     	=							'BlipImageProcessor'
   _SCREAMING_SNAKE_CASE   :					Dict     	=							'AutoTokenizer'


   def __init__(			self      ,    _UpperCamelCase      ,    _UpperCamelCase      ,    _UpperCamelCase  ):





      """simple docstring"""





      super().__init__(_UpperCamelCase      ,    _UpperCamelCase  )

      # add QFormer tokenizer
      _lowercase      :				List[Any]      					=       qformer_tokenizer


   def __call__(			self      ,    _UpperCamelCase = None      ,    _UpperCamelCase = None      ,    _UpperCamelCase = True      ,    _UpperCamelCase = False      ,    _UpperCamelCase = None      ,    _UpperCamelCase = None      ,    _UpperCamelCase = 0      ,    _UpperCamelCase = None      ,    _UpperCamelCase = None      ,    _UpperCamelCase = False      ,    _UpperCamelCase = False      ,    _UpperCamelCase = False      ,    _UpperCamelCase = False      ,    _UpperCamelCase = False      ,    _UpperCamelCase = True      ,    _UpperCamelCase = None      ,    **_UpperCamelCase      ,    ):





      """simple docstring"""





      if images is None and text is None:
         raise ValueError("You have to specify at least images or text."  )

      _lowercase      :				str      					=       BatchFeature()

      if text is not None:
         _lowercase      :				Dict      					=       self.tokenizer(
             text=_UpperCamelCase      ,    add_special_tokens=_UpperCamelCase      ,    padding=_UpperCamelCase      ,    truncation=_UpperCamelCase      ,    max_length=_UpperCamelCase      ,    stride=_UpperCamelCase      ,    pad_to_multiple_of=_UpperCamelCase      ,    return_attention_mask=_UpperCamelCase      ,    return_overflowing_tokens=_UpperCamelCase      ,    return_special_tokens_mask=_UpperCamelCase      ,    return_offsets_mapping=_UpperCamelCase      ,    return_token_type_ids=_UpperCamelCase      ,    return_length=_UpperCamelCase      ,    verbose=_UpperCamelCase      ,    return_tensors=_UpperCamelCase      ,    **_UpperCamelCase      ,    )
         encoding.update(_UpperCamelCase  )
         _lowercase      :				Dict      					=       self.qformer_tokenizer(
             text=_UpperCamelCase      ,    add_special_tokens=_UpperCamelCase      ,    padding=_UpperCamelCase      ,    truncation=_UpperCamelCase      ,    max_length=_UpperCamelCase      ,    stride=_UpperCamelCase      ,    pad_to_multiple_of=_UpperCamelCase      ,    return_attention_mask=_UpperCamelCase      ,    return_overflowing_tokens=_UpperCamelCase      ,    return_special_tokens_mask=_UpperCamelCase      ,    return_offsets_mapping=_UpperCamelCase      ,    return_token_type_ids=_UpperCamelCase      ,    return_length=_UpperCamelCase      ,    verbose=_UpperCamelCase      ,    return_tensors=_UpperCamelCase      ,    **_UpperCamelCase      ,    )
         _lowercase      :				Union[str, Any]      					=       qformer_text_encoding.pop("input_ids"  )
         _lowercase      :				List[Any]      					=       qformer_text_encoding.pop("attention_mask"  )

      if images is not None:
         _lowercase      :				List[Any]      					=       self.image_processor(_UpperCamelCase      ,    return_tensors=_UpperCamelCase  )
         encoding.update(_UpperCamelCase  )

      return encoding


   def 						_lowerCamelCase       (			self      ,    *_UpperCamelCase      ,    **_UpperCamelCase  ):





      """simple docstring"""





      return self.tokenizer.batch_decode(*_UpperCamelCase      ,    **_UpperCamelCase  )


   def 						_lowerCamelCase       (			self      ,    *_UpperCamelCase      ,    **_UpperCamelCase  ):





      """simple docstring"""





      return self.tokenizer.decode(*_UpperCamelCase      ,    **_UpperCamelCase  )


   @property
   # Copied from transformers.models.blip.processing_blip.BlipProcessor.model_input_names
   def 						_lowerCamelCase       (			self  ):





      """simple docstring"""





      _lowercase      :				Dict      					=       self.tokenizer.model_input_names
      _lowercase      :				Optional[Any]      					=       self.image_processor.model_input_names
      return list(dict.fromkeys(tokenizer_input_names + image_processor_input_names  )  )


   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase      ,    **_UpperCamelCase  ):





      """simple docstring"""





      if os.path.isfile(_UpperCamelCase  ):
         raise ValueError(f'''Provided path ({save_directory}) should be a directory, not a file'''  )
      os.makedirs(_UpperCamelCase      ,    exist_ok=_UpperCamelCase  )
      _lowercase      :				Union[str, Any]      					=       os.path.join(_UpperCamelCase      ,    "qformer_tokenizer"  )
      self.qformer_tokenizer.save_pretrained(_UpperCamelCase  )
      return super().save_pretrained(_UpperCamelCase      ,    **_UpperCamelCase  )






   @classmethod
   def 						_lowerCamelCase       (			cls      ,    _UpperCamelCase      ,    **_UpperCamelCase  ):





      """simple docstring"""





      _lowercase      :				List[Any]      					=       AutoTokenizer.from_pretrained(_UpperCamelCase      ,    subfolder="qformer_tokenizer"  )
      _lowercase      :				Optional[Any]      					=       cls._get_arguments_from_pretrained(_UpperCamelCase      ,    **_UpperCamelCase  )
      args.append(_UpperCamelCase  )
      return cls(*_UpperCamelCase  )






