




"""simple docstring"""



from __future__ import annotations

from collections.abc import Callable

SCREAMING_SNAKE_CASE				=       list[list[float | int]]







def   _SCREAMING_SNAKE_CASE   (							lowercase_			, lowercase_						)						->		List[str]:
 A__       =				len(lowerCamelCase_						)
 A__       =				[[0 for _ in range(size + 1						)] for _ in range(lowerCamelCase_						)]
 A__       =				42
 A__       =				42
 A__       =				42
 A__       =				42
 A__       =				42
 A__       =				42

 for row in range(lowerCamelCase_						):
  for col in range(lowerCamelCase_						):
   A__       =				matrix[row][col]

  A__       =				vector[row][0]

 A__       =				0
 A__       =				0
 while row < size and col < size:
  # pivoting
  A__       =				max((abs(augmented[rowa][col]						), rowa) for rowa in range(lowerCamelCase_			, lowerCamelCase_						)						)[
      1
  ]
  if augmented[pivot_row][col] == 0:
   col += 1
   continue
  else:
   A__,      A__       =				augmented[pivot_row], augmented[row]

  for rowa in range(row + 1			, lowerCamelCase_						):
   A__       =				augmented[rowa][col] / augmented[row][col]
   A__       =				0
   for cola in range(col + 1			, size + 1						):
    augmented[rowa][cola] -= augmented[row][cola] * ratio

  row += 1
  col += 1

 # back substitution
 for col in range(1			, lowerCamelCase_						):
  for row in range(lowerCamelCase_						):
   A__       =				augmented[row][col] / augmented[col][col]
   for cola in range(lowerCamelCase_			, size + 1						):
    augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
 return [
     [round(augmented[row][size] / augmented[row][row]			, 10						)] for row in range(lowerCamelCase_						)
 ]







def   _SCREAMING_SNAKE_CASE   (							lowercase_						)						->		Optional[Any]:
 A__       =				len(lowerCamelCase_						)
 A__       =				[[0 for _ in range(lowerCamelCase_						)] for _ in range(lowerCamelCase_						)]
 A__       =				[[0] for _ in range(lowerCamelCase_						)]
 A__       =				42
 A__       =				42
 A__       =				42
 A__       =				42

 for x_val, y_val in enumerate(lowerCamelCase_						):
  for col in range(lowerCamelCase_						):
   A__       =				(x_val + 1) ** (size - col - 1)
  A__       =				y_val

 A__       =				solve(lowerCamelCase_			, lowerCamelCase_						)

 def interpolated_func(lowercase_						) -> int:
  return sum(
      round(coeffs[x_val][0]						) * (var ** (size - x_val - 1))
      for x_val in range(lowerCamelCase_						)						)

 return interpolated_func







def   _SCREAMING_SNAKE_CASE   (							lowercase_						)						->		Dict:
 return (
     1
     - variable
     + variable**2
     - variable**3
     + variable**4
     - variable**5
     + variable**6
     - variable**7
     + variable**8
     - variable**9
     + variable**10
 )







def   _SCREAMING_SNAKE_CASE   (							lowercase_ = question_function			, lowercase_ = 10						)						->		Tuple:
 A__       =				[func(lowerCamelCase_						) for x_val in range(1			, order + 1						)]

 A__       =				[
     interpolate(data_points[:max_coeff]						) for max_coeff in range(1			, order + 1						)
 ]

 A__       =				0
 A__       =				42
 A__       =				42

 for poly in polynomials:
  A__       =				1
  while func(lowerCamelCase_						) == poly(lowerCamelCase_						):
   x_val += 1

  ret += poly(lowerCamelCase_						)

 return ret


if __name__ == "__main__":
      print(f'{solution() = }')













import json
from typing import List, Optional, Tuple

from tokenizers import normalizers

from ...tokenization_utils_fast import PreTrainedTokenizerFast
from ...utils import logging
from .tokenization_distilbert import DistilBertTokenizer


A__	:			List[Any]			   = logging.get_logger(__name__)

A__	:			str			   = {'vocab_file': 'vocab.txt', 'tokenizer_file': 'tokenizer.json'}

A__	:			int			   = {
    'vocab_file': {
        'distilbert-base-uncased': 'https://huggingface.co/distilbert-base-uncased/resolve/main/vocab.txt',
        'distilbert-base-uncased-distilled-squad': (
            'https://huggingface.co/distilbert-base-uncased-distilled-squad/resolve/main/vocab.txt'
        ),
        'distilbert-base-cased': 'https://huggingface.co/distilbert-base-cased/resolve/main/vocab.txt',
        'distilbert-base-cased-distilled-squad': (
            'https://huggingface.co/distilbert-base-cased-distilled-squad/resolve/main/vocab.txt'
        ),
        'distilbert-base-german-cased': 'https://huggingface.co/distilbert-base-german-cased/resolve/main/vocab.txt',
        'distilbert-base-multilingual-cased': (
            'https://huggingface.co/distilbert-base-multilingual-cased/resolve/main/vocab.txt'
        ),
    },
    'tokenizer_file': {
        'distilbert-base-uncased': 'https://huggingface.co/distilbert-base-uncased/resolve/main/tokenizer.json',
        'distilbert-base-uncased-distilled-squad': (
            'https://huggingface.co/distilbert-base-uncased-distilled-squad/resolve/main/tokenizer.json'
        ),
        'distilbert-base-cased': 'https://huggingface.co/distilbert-base-cased/resolve/main/tokenizer.json',
        'distilbert-base-cased-distilled-squad': (
            'https://huggingface.co/distilbert-base-cased-distilled-squad/resolve/main/tokenizer.json'
        ),
        'distilbert-base-german-cased': (
            'https://huggingface.co/distilbert-base-german-cased/resolve/main/tokenizer.json'
        ),
        'distilbert-base-multilingual-cased': (
            'https://huggingface.co/distilbert-base-multilingual-cased/resolve/main/tokenizer.json'
        ),
    },
}

A__	:			Optional[Any]			   = {
    'distilbert-base-uncased': 5_12,
    'distilbert-base-uncased-distilled-squad': 5_12,
    'distilbert-base-cased': 5_12,
    'distilbert-base-cased-distilled-squad': 5_12,
    'distilbert-base-german-cased': 5_12,
    'distilbert-base-multilingual-cased': 5_12,
}


A__	:			List[str]			   = {
    'distilbert-base-uncased': {'do_lower_case': True},
    'distilbert-base-uncased-distilled-squad': {'do_lower_case': True},
    'distilbert-base-cased': {'do_lower_case': False},
    'distilbert-base-cased-distilled-squad': {'do_lower_case': False},
    'distilbert-base-german-cased': {'do_lower_case': False},
    'distilbert-base-multilingual-cased': {'do_lower_case': False},
}
class       _UpperCAmelCase					(       A__	):

				"""simple docstring"""




				lowercase__											=       VOCAB_FILES_NAMES
				lowercase__											=       PRETRAINED_VOCAB_FILES_MAP
				lowercase__											=       PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
				lowercase__											=       PRETRAINED_INIT_CONFIGURATION
				lowercase__											=       ["""input_ids""", """attention_mask"""]
				lowercase__											=       DistilBertTokenizer




				def __init__(     self						:    List[Any],  lowerCamelCase						:    List[Any]=None,  lowerCamelCase						:    Dict=None,  lowerCamelCase						:    str=True,  lowerCamelCase						:    Optional[int]="[UNK]",  lowerCamelCase						:    Optional[Any]="[SEP]",  lowerCamelCase						:    List[Any]="[PAD]",  lowerCamelCase						:    Any="[CLS]",  lowerCamelCase						:    Union[str, Any]="[MASK]",  lowerCamelCase						:    str=True,  lowerCamelCase						:    int=None,  **lowerCamelCase						:    Union[str, Any],  ):

								'''simple docstring'''
								super().__init__(
								    lowerCamelCase,  tokenizer_file=lowerCamelCase,  do_lower_case=lowerCamelCase,  unk_token=lowerCamelCase,  sep_token=lowerCamelCase,  pad_token=lowerCamelCase,  cls_token=lowerCamelCase,  mask_token=lowerCamelCase,  tokenize_chinese_chars=lowerCamelCase,  strip_accents=lowerCamelCase,  **lowerCamelCase,  )

								lowercase__    =			json.loads(self.backend_tokenizer.normalizer.__getstate__()  )
								if (
								    normalizer_state.get('''lowercase''',  lowerCamelCase  ) != do_lower_case
								    or normalizer_state.get('''strip_accents''',  lowerCamelCase  ) != strip_accents
								    or normalizer_state.get('''handle_chinese_chars''',  lowerCamelCase  ) != tokenize_chinese_chars
								):
												lowercase__    =			getattr(lowerCamelCase,  normalizer_state.pop('''type'''  )  )
												lowercase__    =			do_lower_case
												lowercase__    =			strip_accents
												lowercase__    =			tokenize_chinese_chars
												lowercase__    =			normalizer_class(**lowerCamelCase  )

								lowercase__    =			do_lower_case




				def 				lowercase__   (     self						:    str,  lowerCamelCase						:    Optional[Any],  lowerCamelCase						:    List[Any]=None  ):

								'''simple docstring'''
								lowercase__    =			[self.cls_token_id] + token_ids_a + [self.sep_token_id]

								if token_ids_a:
												output += token_ids_a + [self.sep_token_id]

								return output




				def 				lowercase__   (     self						:    Union[str, Any],  lowerCamelCase						:    List[int],  lowerCamelCase						:    Optional[List[int]] = None  ):

								'''simple docstring'''
								lowercase__    =			[self.sep_token_id]
								lowercase__    =			[self.cls_token_id]
								if token_ids_a is None:
												return len(cls + token_ids_a + sep  ) * [0]
								return len(cls + token_ids_a + sep  ) * [0] + len(token_ids_a + sep  ) * [1]




				def 				lowercase__   (     self						:    str,  lowerCamelCase						:    str,  lowerCamelCase						:    Optional[str] = None  ):

								'''simple docstring'''
								lowercase__    =			self._tokenizer.model.save(lowerCamelCase,  name=lowerCamelCase  )
								return tuple(lowerCamelCase  )




