






import json
import os
from functools import lru_cache
from typing import TYPE_CHECKING, List, Optional, Tuple

import regex as re

from ...tokenization_utils import AddedToken, PreTrainedTokenizer
from ...utils import logging


if TYPE_CHECKING:
 from transformers.pipelines.conversational import Conversation

__snake_case							 =  logging.get_logger(__name__)

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

__snake_case							 =  {
    """vocab_file""": {
        """gpt2""": """https://huggingface.co/gpt2/resolve/main/vocab.json""",
        """gpt2-medium""": """https://huggingface.co/gpt2-medium/resolve/main/vocab.json""",
        """gpt2-large""": """https://huggingface.co/gpt2-large/resolve/main/vocab.json""",
        """gpt2-xl""": """https://huggingface.co/gpt2-xl/resolve/main/vocab.json""",
        """distilgpt2""": """https://huggingface.co/distilgpt2/resolve/main/vocab.json""",
    },
    """merges_file""": {
        """gpt2""": """https://huggingface.co/gpt2/resolve/main/merges.txt""",
        """gpt2-medium""": """https://huggingface.co/gpt2-medium/resolve/main/merges.txt""",
        """gpt2-large""": """https://huggingface.co/gpt2-large/resolve/main/merges.txt""",
        """gpt2-xl""": """https://huggingface.co/gpt2-xl/resolve/main/merges.txt""",
        """distilgpt2""": """https://huggingface.co/distilgpt2/resolve/main/merges.txt""",
    },
}

__snake_case							 =  {
    """gpt2""": 10_24,
    """gpt2-medium""": 10_24,
    """gpt2-large""": 10_24,
    """gpt2-xl""": 10_24,
    """distilgpt2""": 10_24,
}


@lru_cache()
def   _A       (    ):
    UpperCamelCase	:Dict     							=       (
        list(range(ord('''!'''	)					,  ord('''~'''	) + 1	)	) + list(range(ord('''¡'''	)					,  ord('''¬'''	) + 1	)	) + list(range(ord('''®'''	)					,  ord('''ÿ'''	) + 1	)	)
    )
    UpperCamelCase	:Union[str, Any]     							=       bs[:]
    UpperCamelCase	:Dict     							=       0
    for b in range(2**8	):
        if b not in bs:
            bs.append(SCREAMING_SNAKE_CASE__	)
            cs.append(2**8 + n	)
            n += 1
    UpperCamelCase	:Any     							=       [chr(SCREAMING_SNAKE_CASE__	) for n in cs]
    return dict(zip(SCREAMING_SNAKE_CASE__					,  SCREAMING_SNAKE_CASE__	)	)


def   _A       (    SCREAMING_SNAKE_CASE__  :     Any	):
    UpperCamelCase	:Union[str, Any]     							=       set()
    UpperCamelCase	:int     							=       word[0]
    for char in word[1:]:
        pairs.add((prev_char, char)	)
        UpperCamelCase	:Dict     							=       char
    return pairs







class       UpperCAmelCase_						( lowercase			):



      """simple docstring"""
      UpperCamelCase_    : Union[str, Any]									=VOCAB_FILES_NAMES
      UpperCamelCase_    : Optional[Any]									=PRETRAINED_VOCAB_FILES_MAP
      UpperCamelCase_    : Dict									=PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
      UpperCamelCase_    : str									=['input_ids', 'attention_mask']
      def __init__(    self   ,    SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_="replace"   ,    SCREAMING_SNAKE_CASE_="<|endoftext|>"   ,    SCREAMING_SNAKE_CASE_="<|endoftext|>"   ,    SCREAMING_SNAKE_CASE_="<|endoftext|>"   ,    SCREAMING_SNAKE_CASE_=None   ,    SCREAMING_SNAKE_CASE_=False   ,    SCREAMING_SNAKE_CASE_=False   ,    **SCREAMING_SNAKE_CASE_   ,    )    ->				Tuple:
          UpperCamelCase	:Dict     							=       AddedToken(SCREAMING_SNAKE_CASE_   ,    lstrip=SCREAMING_SNAKE_CASE_   ,    rstrip=SCREAMING_SNAKE_CASE_			) if isinstance(SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_			) else bos_token
          UpperCamelCase	:Any     							=       AddedToken(SCREAMING_SNAKE_CASE_   ,    lstrip=SCREAMING_SNAKE_CASE_   ,    rstrip=SCREAMING_SNAKE_CASE_			) if isinstance(SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_			) else eos_token
          UpperCamelCase	:Optional[Any]     							=       AddedToken(SCREAMING_SNAKE_CASE_   ,    lstrip=SCREAMING_SNAKE_CASE_   ,    rstrip=SCREAMING_SNAKE_CASE_			) if isinstance(SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_			) else unk_token
          UpperCamelCase	:Dict     							=       AddedToken(SCREAMING_SNAKE_CASE_   ,    lstrip=SCREAMING_SNAKE_CASE_   ,    rstrip=SCREAMING_SNAKE_CASE_			) if isinstance(SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_			) else pad_token
          super().__init__(
              errors=SCREAMING_SNAKE_CASE_   ,    unk_token=SCREAMING_SNAKE_CASE_   ,    bos_token=SCREAMING_SNAKE_CASE_   ,    eos_token=SCREAMING_SNAKE_CASE_   ,    pad_token=SCREAMING_SNAKE_CASE_   ,    add_prefix_space=SCREAMING_SNAKE_CASE_   ,    add_bos_token=SCREAMING_SNAKE_CASE_   ,    **SCREAMING_SNAKE_CASE_   ,    )
          UpperCamelCase	:Tuple     							=       add_bos_token

          with open(SCREAMING_SNAKE_CASE_   ,    encoding='''utf-8'''			) as vocab_handle:
              UpperCamelCase	:Optional[Any]     							=       json.load(SCREAMING_SNAKE_CASE_			)
          UpperCamelCase	:List[Any]     							=       {v: k for k, v in self.encoder.items()}
          UpperCamelCase	:Union[str, Any]     							=       errors  # how to handle errors in decoding
          UpperCamelCase	:List[Any]     							=       bytes_to_unicode()
          UpperCamelCase	:Optional[int]     							=       {v: k for k, v in self.byte_encoder.items()}
          with open(SCREAMING_SNAKE_CASE_   ,    encoding='''utf-8'''			) as merges_handle:
              UpperCamelCase	:List[Any]     							=       merges_handle.read().split('''\n'''			)[1:-1]
          UpperCamelCase	:Dict     							=       [tuple(merge.split()			) for merge in bpe_merges]
          UpperCamelCase	:Optional[Any]     							=       dict(zip(SCREAMING_SNAKE_CASE_   ,    range(len(SCREAMING_SNAKE_CASE_			)			)			)			)
          UpperCamelCase	:List[Any]     							=       {}
          UpperCamelCase	:Optional[int]     							=       add_prefix_space

          # Should have added re.IGNORECASE so BPE merges can happen for capitalized versions of contractions
          UpperCamelCase	:List[str]     							=       re.compile(r'''\'s|\'t|\'re|\'ve|\'m|\'ll|\'d| ?\p{L}+| ?\p{N}+| ?[^\s\p{L}\p{N}]+|\s+(?!\S)|\s+'''			)
      @property
      def    UpperCAmelCase						(    self			)    ->				List[str]:
          return len(self.encoder			)
      def    UpperCAmelCase						(    self			)    ->				Union[str, Any]:
          return dict(self.encoder   ,    **self.added_tokens_encoder			)
      def    UpperCAmelCase						(    self   ,    SCREAMING_SNAKE_CASE_			)    ->				Any:
          if token in self.cache:
              return self.cache[token]
          UpperCamelCase	:int     							=       tuple(SCREAMING_SNAKE_CASE_			)
          UpperCamelCase	:str     							=       get_pairs(SCREAMING_SNAKE_CASE_			)

          if not pairs:
              return token

          while True:
              UpperCamelCase	:int     							=       min(SCREAMING_SNAKE_CASE_   ,    key=lambda SCREAMING_SNAKE_CASE_			: self.bpe_ranks.get(SCREAMING_SNAKE_CASE_   ,    float('''inf'''			)			)			)
              if bigram not in self.bpe_ranks:
                  break
              UpperCamelCase							,       UpperCamelCase	:Any     							=       bigram
              UpperCamelCase	:Union[str, Any]     							=       []
              UpperCamelCase	:List[str]     							=       0
              while i < len(SCREAMING_SNAKE_CASE_			):
                  try:
                      UpperCamelCase	:Tuple     							=       word.index(SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_			)
                  except ValueError:
                      new_word.extend(word[i:]			)
                      break
                  else:
                      new_word.extend(word[i:j]			)
                      UpperCamelCase	:Tuple     							=       j

                  if word[i] == first and i < len(SCREAMING_SNAKE_CASE_			) - 1 and word[i + 1] == second:
                      new_word.append(first + second			)
                      i += 2
                  else:
                      new_word.append(word[i]			)
                      i += 1
              UpperCamelCase	:str     							=       tuple(SCREAMING_SNAKE_CASE_			)
              UpperCamelCase	:Optional[Any]     							=       new_word
              if len(SCREAMING_SNAKE_CASE_			) == 1:
                  break
              else:
                  UpperCamelCase	:List[Any]     							=       get_pairs(SCREAMING_SNAKE_CASE_			)
          UpperCamelCase	:Union[str, Any]     							=       ''' '''.join(SCREAMING_SNAKE_CASE_			)
          UpperCamelCase	:int     							=       word
          return word
      def    UpperCAmelCase						(    self   ,    SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_=None			)    ->				List[str]:
          if self.add_bos_token:
              UpperCamelCase	:Optional[int]     							=       [self.bos_token_id]
          else:
              UpperCamelCase	:str     							=       []

          UpperCamelCase	:Union[str, Any]     							=       bos_token_ids + token_ids_a

          if token_ids_a is None:
              return output

          return output + bos_token_ids + token_ids_a
      def    UpperCAmelCase						(    self   ,    SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_ = None   ,    SCREAMING_SNAKE_CASE_ = False			)    ->				List[int]:
          if already_has_special_tokens:
              return super().get_special_tokens_mask(
                  token_ids_a=SCREAMING_SNAKE_CASE_   ,    token_ids_a=SCREAMING_SNAKE_CASE_   ,    already_has_special_tokens=SCREAMING_SNAKE_CASE_			)

          if not self.add_bos_token:
              return super().get_special_tokens_mask(
                  token_ids_a=SCREAMING_SNAKE_CASE_   ,    token_ids_a=SCREAMING_SNAKE_CASE_   ,    already_has_special_tokens=SCREAMING_SNAKE_CASE_			)

          if token_ids_a is None:
              return [1] + ([0] * len(SCREAMING_SNAKE_CASE_			))
          return [1] + ([0] * len(SCREAMING_SNAKE_CASE_			)) + [1] + ([0] * len(SCREAMING_SNAKE_CASE_			))
      def    UpperCAmelCase						(    self   ,    SCREAMING_SNAKE_CASE_			)    ->				Any:
          UpperCamelCase	:Any     							=       []
          for token in re.findall(self.pat   ,    SCREAMING_SNAKE_CASE_			):
              UpperCamelCase	:int     							=       ''''''.join(
                  self.byte_encoder[b] for b in token.encode('''utf-8'''			)			)  # Maps all our bytes to unicode strings, avoiding control tokens of the BPE (spaces in our case)
              bpe_tokens.extend(bpe_token for bpe_token in self.bpe(SCREAMING_SNAKE_CASE_			).split(''' '''			)			)
          return bpe_tokens
      def    UpperCAmelCase						(    self   ,    SCREAMING_SNAKE_CASE_			)    ->				Union[str, Any]:
          return self.encoder.get(SCREAMING_SNAKE_CASE_   ,    self.encoder.get(self.unk_token			)			)
      def    UpperCAmelCase						(    self   ,    SCREAMING_SNAKE_CASE_			)    ->				Optional[Any]:
          return self.decoder.get(SCREAMING_SNAKE_CASE_			)
      def    UpperCAmelCase						(    self   ,    SCREAMING_SNAKE_CASE_			)    ->				Optional[Any]:
          UpperCamelCase	:Union[str, Any]     							=       ''''''.join(SCREAMING_SNAKE_CASE_			)
          UpperCamelCase	:Optional[int]     							=       bytearray([self.byte_decoder[c] for c in text]			).decode('''utf-8'''   ,    errors=self.errors			)
          return text
      def    UpperCAmelCase						(    self   ,    SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_ = None			)    ->				Tuple[str]:
          if not os.path.isdir(SCREAMING_SNAKE_CASE_			):
              logger.error(F'''Vocabulary path ({save_directory}) should be a directory'''			)
              return
          UpperCamelCase	:Optional[Any]     							=       os.path.join(
              SCREAMING_SNAKE_CASE_   ,    (filename_prefix + '''-''' if filename_prefix else '''''') + VOCAB_FILES_NAMES['''vocab_file''']			)
          UpperCamelCase	:Any     							=       os.path.join(
              SCREAMING_SNAKE_CASE_   ,    (filename_prefix + '''-''' if filename_prefix else '''''') + VOCAB_FILES_NAMES['''merges_file''']			)

          with open(SCREAMING_SNAKE_CASE_   ,    '''w'''   ,    encoding='''utf-8'''			) as f:
              f.write(json.dumps(self.encoder   ,    indent=2   ,    sort_keys=SCREAMING_SNAKE_CASE_   ,    ensure_ascii=SCREAMING_SNAKE_CASE_			) + '''\n'''			)

          UpperCamelCase	:List[Any]     							=       0
          with open(SCREAMING_SNAKE_CASE_   ,    '''w'''   ,    encoding='''utf-8'''			) as writer:
              writer.write('''#version: 0.2\n'''			)
              for bpe_tokens, token_index in sorted(self.bpe_ranks.items()   ,    key=lambda SCREAMING_SNAKE_CASE_			: kv[1]			):
                  if index != token_index:
                      logger.warning(
                          F'''Saving vocabulary to {merge_file}: BPE merge indices are not consecutive.'''
                          ''' Please check that the tokenizer is not corrupted!'''			)
                      UpperCamelCase	:Optional[Any]     							=       token_index
                  writer.write(''' '''.join(SCREAMING_SNAKE_CASE_			) + '''\n'''			)
                  index += 1

          return vocab_file, merge_file
      def    UpperCAmelCase						(    self   ,    SCREAMING_SNAKE_CASE_   ,    SCREAMING_SNAKE_CASE_=False   ,    **SCREAMING_SNAKE_CASE_			)    ->				Optional[Any]:
          UpperCamelCase	:Optional[int]     							=       kwargs.pop('''add_prefix_space'''   ,    self.add_prefix_space			)
          if is_split_into_words or add_prefix_space:
              UpperCamelCase	:str     							=       ''' ''' + text
          return (text, kwargs)




      def    UpperCAmelCase						(    self   ,    SCREAMING_SNAKE_CASE_			)    ->				List[int]:
          UpperCamelCase	:str     							=       []
          for is_user, text in conversation.iter_texts():
              input_ids.extend(self.encode(SCREAMING_SNAKE_CASE_   ,    add_special_tokens=SCREAMING_SNAKE_CASE_			) + [self.eos_token_id]			)
          if len(SCREAMING_SNAKE_CASE_			) > self.model_max_length:
              UpperCamelCase	:Union[str, Any]     							=       input_ids[-self.model_max_length :]
          return input_ids













def   _A       (    SCREAMING_SNAKE_CASE__  :     list[list[int]]	):
    if len(SCREAMING_SNAKE_CASE__	) == 0 or not all(len(SCREAMING_SNAKE_CASE__	) == 2 for pair in coordinates	):
        raise ValueError('''The program cannot work out a fitting polynomial.'''	)

    if len({tuple(SCREAMING_SNAKE_CASE__	) for pair in coordinates}	) != len(SCREAMING_SNAKE_CASE__	):
        raise ValueError('''The program cannot work out a fitting polynomial.'''	)

    UpperCamelCase	:str     							=       {x for x, _ in coordinates}
    if len(SCREAMING_SNAKE_CASE__	) == 1:
        return F'''x={coordinates[0][0]}'''

    if len(SCREAMING_SNAKE_CASE__	) != len(SCREAMING_SNAKE_CASE__	):
        raise ValueError('''The program cannot work out a fitting polynomial.'''	)

    UpperCamelCase	:List[Any]     							=       len(SCREAMING_SNAKE_CASE__	)

    UpperCamelCase	:Optional[int]     							=       0
    UpperCamelCase	:list[list[float]]     							=       []
    # put the x and x to the power values in a matrix
    while count_of_line < x:
        UpperCamelCase	:Tuple     							=       0
        UpperCamelCase	:Optional[int]     							=       coordinates[count_of_line][0]
        UpperCamelCase	:list[float]     							=       []
        while count_in_line < x:
            count_line.append(a ** (x - (count_in_line + 1))	)
            count_in_line += 1
        matrix.append(SCREAMING_SNAKE_CASE__	)
        count_of_line += 1

    UpperCamelCase	:Optional[int]     							=       0
    # put the y values into a vector
    UpperCamelCase	:list[float]     							=       []
    while count_of_line < x:
        vector.append(coordinates[count_of_line][1]	)
        count_of_line += 1

    UpperCamelCase	:str     							=       0

    while count < x:
        UpperCamelCase	:Optional[Any]     							=       0
        while zahlen < x:
            if count == zahlen:
                zahlen += 1
            if zahlen == x:
                break
            UpperCamelCase	:Union[str, Any]     							=       matrix[zahlen][count] / matrix[count][count]
            for counting_columns, item in enumerate(matrix[count]	):
                # manipulating all the values in the matrix
                matrix[zahlen][counting_columns] -= item * bruch
            # manipulating the values in the vector
            vector[zahlen] -= vector[count] * bruch
            zahlen += 1
        count += 1

    UpperCamelCase	:Optional[int]     							=       0
    # make solutions
    UpperCamelCase	:list[str]     							=       []
    while count < x:
        solution.append(str(vector[count] / matrix[count][count]	)	)
        count += 1

    UpperCamelCase	:Union[str, Any]     							=       0
    UpperCamelCase	:Any     							=       '''f(x)='''

    while count < x:
        UpperCamelCase	:list[str]     							=       solution[count].split('''E'''	)
        if len(SCREAMING_SNAKE_CASE__	) > 1:
            UpperCamelCase	:List[Any]     							=       F'''{remove_e[0]}*10^{remove_e[1]}'''
        solved += F'''x^{x - (count + 1)}*{solution[count]}'''
        if count + 1 != x:
            solved += "+"
        count += 1

    return solved


if __name__ == "__main__":
 print(points_to_polynomial([]))
 print(points_to_polynomial([[]]))
 print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
 print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
 print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
 print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
 print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
 print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
 print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
 print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))





