
import mpmath  # for roots of unity
import numpy as np
class 		UpperCamelCase__  :
   def __init__(self			: Tuple ,    snake_case_			: Union[str, Any]=None ,    snake_case_			: Optional[Any]=None       ):
    __a			:  Optional[Any]		    =  list(poly_a or [0]       )[:]
    __a			:  Any		    =  list(poly_b or [0]       )[:]

    # Remove leading zero coefficients
    while self.polyA[-1] == 0:
     self.polyA.pop()
    __a			:  Optional[int]		    =  len(self.polyA       )

    while self.polyB[-1] == 0:
     self.polyB.pop()
    __a			:  Any		    =  len(self.polyB       )

    # Add 0 to make lengths equal a power of 2
    __a			:  str		    =  int(
        2 ** np.ceil(np.loga(len(self.polyA       ) + len(self.polyB       ) - 1       )       )       )

    while len(self.polyA       ) < self.c_max_length:
     self.polyA.append(0       )
    while len(self.polyB       ) < self.c_max_length:
     self.polyB.append(0       )
    # A complex root used for the fourier transform
    __a			:  str		    =  complex(mpmath.root(x=1 ,    n=self.c_max_length ,    k=1       )       )

    # The product
    __a			:  int		    =  self.__multiply()
   def 				lowerCAmelCase      (self			: Optional[Any] ,    snake_case_			: List[str]       ):
    __a			:  List[Any]		    =  [[x] for x in self.polyA] if which == 'A' else [[x] for x in self.polyB]
    # Corner case
    if len(_A       ) <= 1:
     return dft[0]
    #
    __a			:  Union[str, Any]		    =  self.c_max_length // 2
    while next_ncol > 0:
     __a			:  List[Any]		    =  [[] for i in range(_A       )]
     __a			:  Any		    =  self.root**next_ncol

     # First half of next step
     __a			:  Tuple		    =  1
     for j in range(self.c_max_length // (next_ncol * 2)       ):
      for i in range(_A       ):
       new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]       )
      current_root *= root
     # Second half of next step
     __a			:  Optional[Any]		    =  1
     for j in range(self.c_max_length // (next_ncol * 2)       ):
      for i in range(_A       ):
       new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]       )
      current_root *= root
     # Update
     __a			:  List[str]		    =  new_dft
     __a			:  Any		    =  next_ncol // 2
    return dft[0]
   def 				lowerCAmelCase      (self			: List[str]       ):
    __a			:  Any		    =  self.__dft('''A'''       )
    __a			:  Optional[Any]		    =  self.__dft('''B'''       )
    __a			:  Tuple		    =  [[dft_a[i] * dft_b[i] for i in range(self.c_max_length       )]]
    del dft_a
    del dft_b

    # Corner Case
    if len(inverce_c[0]       ) <= 1:
     return inverce_c[0]
    # Inverse DFT
    __a			:  str		    =  2
    while next_ncol <= self.c_max_length:
     __a			:  Union[str, Any]		    =  [[] for i in range(_A       )]
     __a			:  List[str]		    =  self.root ** (next_ncol // 2)
     __a			:  Optional[int]		    =  1
     # First half of next step
     for j in range(self.c_max_length // next_ncol       ):
      for i in range(next_ncol // 2       ):
       # Even positions
       new_inverse_c[i].append(
           (
               inverce_c[i][j]
               + inverce_c[i][j + self.c_max_length // next_ncol]
           )
           / 2       )
       # Odd positions
       new_inverse_c[i + next_ncol // 2].append(
           (
               inverce_c[i][j]
               - inverce_c[i][j + self.c_max_length // next_ncol]
           )
           / (2 * current_root)       )
      current_root *= root
     # Update
     __a			:  List[str]		    =  new_inverse_c
     next_ncol *= 2
    # Unpack
    __a			:  List[str]		    =  [round(x[0].real ,    8       ) + round(x[0].imag ,    8       ) * 1J for x in inverce_c]

    # Remove leading 0's
    while inverce_c[-1] == 0:
     inverce_c.pop()
    return inverce_c







   def __str__(self			: Union[str, Any]       ):
    __a			:  List[Any]		    =  'A = ' + ' + '.join(
        f"{coef}*x^{i}" for coef, i in enumerate(self.polyA[: self.len_A]       )       )
    __a			:  List[Any]		    =  'B = ' + ' + '.join(
        f"{coef}*x^{i}" for coef, i in enumerate(self.polyB[: self.len_B]       )       )
    __a			:  Optional[int]		    =  'A*B = ' + ' + '.join(
        f"{coef}*x^{i}" for coef, i in enumerate(self.product       )       )

    return f"{a}\n{b}\n{c}"


# Unit tests
if __name__ == "__main__":
      import doctest

      doctest.testmod()


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        __UpperCamelCase					(    lowerCAmelCase__							:    Union[str, Any]  ,       lowerCAmelCase__							:    int  ,       lowerCAmelCase__							:    List[str]  ,       lowerCAmelCase__							:    Any  ):
 if isinstance(lowerCAmelCase__  ,       lowerCAmelCase__  ):
  __a			:  Union[str, Any]		    =  np.full((len(lowerCAmelCase__  ), sequence_length, 2)  ,       lowerCAmelCase__  )
 else:
  __a			:  str		    =  np.full((len(lowerCAmelCase__  ), sequence_length)  ,       lowerCAmelCase__  )

 for i, tensor in enumerate(lowerCAmelCase__  ):
  if padding_side == "right":
   if isinstance(lowerCAmelCase__  ,       lowerCAmelCase__  ):
    __a			:  Any		    =  tensor[:sequence_length]
   else:
    __a			:  List[Any]		    =  tensor[:sequence_length]
  else:
   if isinstance(lowerCAmelCase__  ,       lowerCAmelCase__  ):
    __a			:  Dict		    =  tensor[:sequence_length]
   else:
    __a			:  int		    =  tensor[:sequence_length]

 return out_tensor.tolist()




def        __UpperCamelCase					(    lowerCAmelCase__							:    Optional[Any]  ):
 __a			:  str		    =  ord(lowerCAmelCase__  )
 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
 __a			:  List[str]		    =  unicodedata.category(lowerCAmelCase__  )
 if cat.startswith('''P'''  ):
  return True
 return False



@dataclass
class 		UpperCamelCase__  (	__lowercase   ):
   _SCREAMING_SNAKE_CASE				:							PreTrainedTokenizerBase
   _SCREAMING_SNAKE_CASE				:							Union[bool, str, PaddingStrategy]     	=				True
   _SCREAMING_SNAKE_CASE				:							Optional[int]     	=				None
   _SCREAMING_SNAKE_CASE				:							Optional[int]     	=				None
   _SCREAMING_SNAKE_CASE				:							int     	=				-100
   _SCREAMING_SNAKE_CASE				:							str     	=				"pt"
   def 				lowerCAmelCase      (self			: str ,    snake_case_			: Tuple       ):
    import torch

    __a			:  Union[str, Any]		    =  '''label''' if '''label''' in features[0].keys() else '''labels'''
    __a			:  Tuple		    =  [feature[label_name] for feature in features] if label_name in features[0].keys() else None
    __a			:  Union[str, Any]		    =  self.tokenizer.pad(
        snake_case_ ,    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

    __a			:  List[str]		    =  torch.tensor(batch['''entity_ids''']       ).shape[1]
    __a			:  Tuple		    =  self.tokenizer.padding_side
    if padding_side == "right":
     __a			:  Union[str, Any]		    =  [
         list(snake_case_       ) + [self.label_pad_token_id] * (sequence_length - len(snake_case_       )) for label in labels
     ]
    else:
     __a			:  Dict		    =  [
         [self.label_pad_token_id] * (sequence_length - len(snake_case_       )) + list(snake_case_       ) for label in labels
     ]

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

    return batch
