


'''simple docstring'''


from math import factorial






class 		lowerCAmelCase__	:




			def __init__(						self     :   Union[str, Any]		,     lowerCamelCase__     :   int		,     lowerCamelCase__     :   Tuple       )      ->Any:



					'''simple docstring'''







					_UpperCAmelCase						:				Dict	    =					real
					if isinstance(A_		,     A_       ):
							_UpperCAmelCase						:				int	    =					[1] * rank
					else:
							_UpperCAmelCase						:				Optional[Any]	    =					rank




			def __repr__(						self     :   int       )      ->List[str]:



					'''simple docstring'''







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




			def 							lowerCAmelCase__			(						self     :   Any       )      ->Optional[int]:



					'''simple docstring'''







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




			def __add__(						self     :   Tuple		,     lowerCamelCase__     :   Dict       )      ->str:



					'''simple docstring'''







					if not isinstance(A_		,     A_       ):
							return Dual(self.real + other		,     self.duals       )
					_UpperCAmelCase						:				Any	    =					self.duals.copy()
					_UpperCAmelCase						:				str	    =					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_       ))       )
					_UpperCAmelCase						:				List[Any]	    =					[]
					for i in range(len(A_       )       ):
							new_duals.append(s_dual[i] + o_dual[i]       )
					return Dual(self.real + other.real		,     A_       )

			lowerCAmelCase       :		List[Any]				      =   __add__




			def __sub__(						self     :   Optional[int]		,     lowerCamelCase__     :   Union[str, Any]       )      ->List[Any]:



					'''simple docstring'''







					return self + other * -1




			def __mul__(						self     :   int		,     lowerCamelCase__     :   Dict       )      ->str:



					'''simple docstring'''







					if not isinstance(A_		,     A_       ):
							_UpperCAmelCase						:				List[Any]	    =					[]
							for i in self.duals:
									new_duals.append(i * other       )
							return Dual(self.real * other		,     A_       )
					_UpperCAmelCase						:				List[str]	    =					[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_       )

			lowerCAmelCase       :		Tuple				      =   __mul__




			def __truediv__(						self     :   Any		,     lowerCamelCase__     :   Dict       )      ->Tuple:



					'''simple docstring'''







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




			def __floordiv__(						self     :   int		,     lowerCamelCase__     :   Union[str, Any]       )      ->Union[str, Any]:



					'''simple docstring'''







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






			def __pow__(						self     :   Union[str, Any]		,     lowerCamelCase__     :   Dict       )      ->Optional[int]:



					'''simple docstring'''







					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
					_UpperCAmelCase						:				Optional[Any]	    =					self
					for _ in range(n - 1       ):
							x *= self
					return x






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


if __name__ == "__main__":
						import doctest

						doctest.testmod()






						def        __lowerCAmelCase       (__lowerCAmelCase      ):
								return y**2 * y**4





						print(differentiate(f, 9, 2))






import unicodedata
from dataclasses import dataclass
from typing import Optional, Union

import numpy as np

from transformers.data.data_collator import DataCollatorMixin
from transformers.file_utils import PaddingStrategy
from transformers.tokenization_utils_base import PreTrainedTokenizerBase







def 		_lowercase (     lowercase__   ,	lowercase__   ,	lowercase__   ,	lowercase__						):
      if isinstance(lowercase__   ,	lowercase__						):
            __lowerCAmelCase					:						Dict					=					np.full((len(lowercase__						), sequence_length, 2)   ,	lowercase__						)
      else:
            __lowerCAmelCase					:						Optional[int]					=					np.full((len(lowercase__						), sequence_length)   ,	lowercase__						)

      for i, tensor in enumerate(lowercase__						):
            if padding_side == "right":
                  if isinstance(lowercase__   ,	lowercase__						):
                        __lowerCAmelCase					:						Union[str, Any]					=					tensor[:sequence_length]
                  else:
                        __lowerCAmelCase					:						int					=					tensor[:sequence_length]
            else:
                  if isinstance(lowercase__   ,	lowercase__						):
                        __lowerCAmelCase					:						Union[str, Any]					=					tensor[:sequence_length]
                  else:
                        __lowerCAmelCase					:						Optional[Any]					=					tensor[:sequence_length]

      return out_tensor.tolist()







def 		_lowercase (     lowercase__						):
      __lowerCAmelCase					:						Union[str, Any]					=					ord(lowercase__						)
      if (cp >= 3_3 and cp <= 4_7) or (cp >= 5_8 and cp <= 6_4) or (cp >= 9_1 and cp <= 9_6) or (cp >= 1_2_3 and cp <= 1_2_6):
            return True
      __lowerCAmelCase					:						int					=					unicodedata.category(lowercase__						)
      if cat.startswith('''P'''						):
            return True
      return False







@dataclass
class   __lowercase      (_UpperCAmelCase ):
 _UpperCamelCase			  =  42
 _UpperCamelCase			  =  True
 _UpperCamelCase			  =  None
 _UpperCamelCase			  =  None
 _UpperCamelCase			  =  -100
 _UpperCamelCase			  =  "pt"
 def 	UpperCamelCase__  (							self      ,							A_					)					->Optional[int]:



       '''simple docstring'''





       import torch

       __lowerCAmelCase					:						List[str]					=					'''label''' if '''label''' in features[0].keys() else '''labels'''
       __lowerCAmelCase					:						Union[str, Any]					=					[feature[label_name] for feature in features] if label_name in features[0].keys() else None
       __lowerCAmelCase					:						List[Any]					=					self.tokenizer.pad(
           A_      ,							padding=self.padding      ,							max_length=self.max_length      ,							pad_to_multiple_of=self.pad_to_multiple_of      ,							return_tensors='''pt''' if labels is None else None      ,							)

       if labels is None:
             return batch

       __lowerCAmelCase					:						Dict					=					torch.tensor(batch['''entity_ids''']					).shape[1]
       __lowerCAmelCase					:						Optional[int]					=					self.tokenizer.padding_side
       if padding_side == "right":
             __lowerCAmelCase					:						Any					=					[
                 list(A_					) + [self.label_pad_token_id] * (sequence_length - len(A_					)) for label in labels
             ]
       else:
             __lowerCAmelCase					:						Optional[int]					=					[
                 [self.label_pad_token_id] * (sequence_length - len(A_					)) + list(A_					) for label in labels
             ]

       __lowerCAmelCase					:						Tuple					=					[feature['''ner_tags'''] for feature in features]
       __lowerCAmelCase					:						List[Any]					=					padding_tensor(A_      ,							-1      ,							A_      ,							A_					)
       __lowerCAmelCase					:						Optional[int]					=					[feature['''original_entity_spans'''] for feature in features]
       __lowerCAmelCase					:						Any					=					padding_tensor(A_      ,							(-1, -1)      ,							A_      ,							A_					)
       __lowerCAmelCase					:						Optional[Any]					=					{k: torch.tensor(A_      ,							dtype=torch.intaa					) for k, v in batch.items()}

       return batch


