

def      snake_case__      (   SCREAMING_SNAKE_CASE_		:   int      ):



     '''simple docstring'''





     lowercase__   :       Dict				=	current_set.copy()
     for row_index, row in enumerate(__UpperCAmelCase      ):
          lowercase__   :       Dict				=	row[0]
          for column_index, column in enumerate(__UpperCAmelCase      ):
               if magnitude == 0:
                    lowercase__   :       Optional[Any]				=	column
                    continue
               lowercase__   :       Optional[Any]				=	column / magnitude
    # Subtract to cancel term
     lowercase__   :       Union[str, Any]				=	current_set[0]
     lowercase__   :       str				=	[first_row]
     lowercase__   :       List[str]				=	current_set[1::]
     for row in current_set:
          lowercase__   :       Dict				=	[]
          # If first term is 0, it is already in form we want, so we preserve it
          if row[0] == 0:
               final_set.append(__UpperCAmelCase      )
               continue
          for column_index in range(len(__UpperCAmelCase      )      ):
               temp_row.append(first_row[column_index] - row[column_index]      )
          final_set.append(__UpperCAmelCase      )
     # Create next recursion iteration set
     if len(final_set[0]      ) != 3:
          lowercase__   :       str				=	final_set[0]
          lowercase__   :       Tuple				=	[]
          lowercase__   :       Any				=	[]
          for row in final_set[1::]:
               current_first_column.append(row[0]      )
               next_iteration.append(row[1::]      )
          lowercase__   :       Tuple				=	simplify(__UpperCAmelCase      )
          for i in range(len(__UpperCAmelCase      )      ):
               resultant[i].insert(0     ,					current_first_column[i]      )
          resultant.insert(0     ,					__UpperCAmelCase      )
          lowercase__   :       Optional[Any]				=	resultant
     return final_set

def      snake_case__      (   SCREAMING_SNAKE_CASE_		:   Dict      ):



     '''simple docstring'''





     if len(__UpperCAmelCase      ) == 0:
          raise IndexError('solve_simultaneous() requires n lists of length n+1'      )
     lowercase__   :       Any				=	len(__UpperCAmelCase      ) + 1
     if any(len(__UpperCAmelCase      ) != _length for item in equations      ):
          raise IndexError('solve_simultaneous() requires n lists of length n+1'      )
     for row in equations:
          if any(not isinstance(__UpperCAmelCase     ,					(int, float)      ) for column in row      ):
               raise ValueError('solve_simultaneous() requires lists of integers'      )
     if len(__UpperCAmelCase      ) == 1:
          return [equations[0][-1] / equations[0][0]]
     lowercase__   :       Optional[int]				=	equations.copy()
     if any(0 in row for row in data_set      ):
          lowercase__   :       Any				=	data_set.copy()
          lowercase__   :       List[Any]				=	[]
          for row_index, row in enumerate(__UpperCAmelCase      ):
               if 0 not in row:
                    lowercase__   :       Tuple				=	data_set.pop(__UpperCAmelCase      )
                    break
          if not full_row:
               raise ValueError('solve_simultaneous() requires at least 1 full equation'      )
          data_set.insert(0     ,					__UpperCAmelCase      )
     lowercase__   :       List[Any]				=	data_set.copy()
     lowercase__   :       List[Any]				=	simplify(__UpperCAmelCase      )
     lowercase__   :       Tuple				=	simplified[::-1]
     lowercase__   :       Tuple				=	[]
     for row in simplified:
          lowercase__   :       Dict				=	row[-1]
          if not solutions:
               if row[-2] == 0:
                    solutions.append(0      )
                    continue
               solutions.append(current_solution / row[-2]      )
               continue
          lowercase__   :       Optional[Any]				=	row.copy()[: len(__UpperCAmelCase      ) - 1 :]
          while temp_row[0] == 0:
               temp_row.pop(0      )
          if len(__UpperCAmelCase      ) == 0:
               solutions.append(0      )
               continue
          lowercase__   :       Optional[Any]				=	temp_row[1::]
          lowercase__   :       Optional[int]				=	temp_row[::-1]
          for column_index, column in enumerate(__UpperCAmelCase      ):
               current_solution -= column * solutions[column_index]
          solutions.append(__UpperCAmelCase      )
     lowercase__   :       str				=	[]
     for item in solutions:
          final.append(float(round(__UpperCAmelCase     ,					5      )      )      )
     return final[::-1]


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       snake_case_        =			[
           [2, 1, 1, 1, 1, 4],
           [1, 2, 1, 1, 1, 5],
           [1, 1, 2, 1, 1, 6],
           [1, 1, 1, 2, 1, 7],
           [1, 1, 1, 1, 2, 8],
       ]
       print(solve_simultaneous(eq))
       print(solve_simultaneous([[4, 2]]))




import json
from typing import TYPE_CHECKING, List, Optional, Tuple

from tokenizers import pre_tokenizers

from ...tokenization_utils_base import BatchEncoding
from ...tokenization_utils_fast import PreTrainedTokenizerFast
from ...utils import logging
from .tokenization_gpta import GPTaTokenizer


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''', '''tokenizer_file''': '''tokenizer.json'''}

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''',
    },
    '''tokenizer_file''': {
        '''gpt2''': '''https://huggingface.co/gpt2/resolve/main/tokenizer.json''',
        '''gpt2-medium''': '''https://huggingface.co/gpt2-medium/resolve/main/tokenizer.json''',
        '''gpt2-large''': '''https://huggingface.co/gpt2-large/resolve/main/tokenizer.json''',
        '''gpt2-xl''': '''https://huggingface.co/gpt2-xl/resolve/main/tokenizer.json''',
        '''distilgpt2''': '''https://huggingface.co/distilgpt2/resolve/main/tokenizer.json''',
    },
}

snake_case_        =			{
    '''gpt2''': 1_024,
    '''gpt2-medium''': 1_024,
    '''gpt2-large''': 1_024,
    '''gpt2-xl''': 1_024,
    '''distilgpt2''': 1_024,
}


class 				SCREAMING_SNAKE_CASE__ (__snake_case					):
    __lowerCamelCase						:	List[str]														=					VOCAB_FILES_NAMES
    __lowerCamelCase						:	Any														=					PRETRAINED_VOCAB_FILES_MAP
    __lowerCamelCase						:	str														=					PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
    __lowerCamelCase						:	int														=					["""input_ids""", """attention_mask"""]
    __lowerCamelCase						:	str														=					GPTaTokenizer





    def __init__(				self						,       a=None						,       a=None						,       a=None						,       a="<|endoftext|>"						,       a="<|endoftext|>"						,       a="<|endoftext|>"						,       a=False						,       **a						,       ):
         super().__init__(
             a						,       a						,       tokenizer_file=a						,       unk_token=a						,       bos_token=a						,       eos_token=a						,       add_prefix_space=a						,       **a						,       )

         lowercase__   :       int				=	kwargs.pop('add_bos_token'						,       a)

         lowercase__   :       List[str]				=	json.loads(self.backend_tokenizer.pre_tokenizer.__getstate__())
         if pre_tok_state.get('add_prefix_space'						,       a) != add_prefix_space:
              lowercase__   :       Optional[Any]				=	getattr(a						,       pre_tok_state.pop('type'))
              lowercase__   :       List[Any]				=	add_prefix_space
              lowercase__   :       str				=	pre_tok_class(**a)

         lowercase__   :       Tuple				=	add_prefix_space





    def 				snake_case_    (				self						,       *a						,       **a):
         lowercase__   :       Tuple				=	kwargs.get('is_split_into_words'						,       a)
         assert self.add_prefix_space or not is_split_into_words, (
             f"""You need to instantiate {self.__class__.__name__} with add_prefix_space=True """
             "to use it with pretokenized inputs."
         )

         return super()._batch_encode_plus(*a						,       **a)





    def 				snake_case_    (				self						,       *a						,       **a):
         lowercase__   :       Optional[Any]				=	kwargs.get('is_split_into_words'						,       a)

         assert self.add_prefix_space or not is_split_into_words, (
             f"""You need to instantiate {self.__class__.__name__} with add_prefix_space=True """
             "to use it with pretokenized inputs."
         )

         return super()._encode_plus(*a						,       **a)





    def 				snake_case_    (				self						,       a						,       a = None):
         lowercase__   :       Any				=	self._tokenizer.model.save(a						,       name=a)
         return tuple(a)





    def 				snake_case_    (				self						,       a):
         lowercase__   :       Union[str, Any]				=	[]
         for is_user, text in conversation.iter_texts():
              input_ids.extend(self.encode(a						,       add_special_tokens=a) + [self.eos_token_id])

         if len(a) > self.model_max_length:
              lowercase__   :       Union[str, Any]				=	input_ids[-self.model_max_length :]
         return input_ids

