



'''simple docstring'''




from __future__ import annotations

from collections.abc import Callable

lowerCamelCase							:Union[str, Any]				    =					list[list[float | int]]



def 	a			( lowerCamelCase__						,      lowerCamelCase__    ):
			'''simple docstring'''





			A_	:						int	=     len(lowerCAmelCase__    )
			A_	:						Matrix	=     [[0 for _ in range(size + 1    )] for _ in range(lowerCAmelCase__    )]
			A_	:						int
			A_	:						int
			A_	:						int
			A_	:						int
			A_	:						int
			A_	:						float

			for row in range(lowerCAmelCase__    ):
						for col in range(lowerCAmelCase__    ):
									A_	:						Optional[Any]	=     matrix[row][col]

						A_	:						Tuple	=     vector[row][0]

			A_	:						Any	=     0
			A_	:						int	=     0
			while row < size and col < size:
						# pivoting
						A_	:						List[str]	=     max((abs(augmented[rowa][col]    ), rowa) for rowa in range(lowerCAmelCase__						,      lowerCAmelCase__    )    )[
						    1
						]
						if augmented[pivot_row][col] == 0:
									col += 1
									continue
						else:
									A_	:						List[str]	=     augmented[pivot_row], augmented[row]

						for rowa in range(row + 1						,      lowerCAmelCase__    ):
									A_	:						List[Any]	=     augmented[rowa][col] / augmented[row][col]
									A_	:						str	=     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_	:						int	=     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 	a			( lowerCamelCase__    ):
			'''simple docstring'''





			A_	:						int	=     len(lowerCAmelCase__    )
			A_	:						Matrix	=     [[0 for _ in range(lowerCAmelCase__    )] for _ in range(lowerCAmelCase__    )]
			A_	:						Matrix	=     [[0] for _ in range(lowerCAmelCase__    )]
			A_	:						Matrix
			A_	:						int
			A_	:						int
			A_	:						int

			for x_val, y_val in enumerate(lowerCAmelCase__    ):
						for col in range(lowerCAmelCase__    ):
									A_	:						Optional[Any]	=     (x_val + 1) ** (size - col - 1)
						A_	:						Union[str, Any]	=     y_val

			A_	:						Any	=     solve(lowerCAmelCase__						,      lowerCAmelCase__    )

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

			return interpolated_func



def 	a			( lowerCamelCase__    ):
			'''simple docstring'''





			return (
			    1
			    - variable
			    + variable**2
			    - variable**3
			    + variable**4
			    - variable**5
			    + variable**6
			    - variable**7
			    + variable**8
			    - variable**9
			    + variable**10
			)



def 	a			( lowerCamelCase__ = question_function						,      lowerCamelCase__ = 10    ):
			'''simple docstring'''





			A_	:						list[int]	=     [func(lowerCAmelCase__    ) for x_val in range(1						,      order + 1    )]

			A_	:						list[Callable[[int], int]]	=     [
			    interpolate(data_points[:max_coeff]    ) for max_coeff in range(1						,      order + 1    )
			]

			A_	:						int	=     0
			A_	:						Callable[[int], int]
			A_	:						int

			for poly in polynomials:
						A_	:						List[str]	=     1
						while func(lowerCAmelCase__    ) == poly(lowerCAmelCase__    ):
									x_val += 1

						ret += poly(lowerCAmelCase__    )

			return ret


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



'''simple docstring'''
from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


UpperCamelCase__    					=      {
    '''configuration_rembert''': ['''REMBERT_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''RemBertConfig''', '''RemBertOnnxConfig''']
}

try:
  if not is_sentencepiece_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCamelCase__    					=      ['''RemBertTokenizer''']

try:
  if not is_tokenizers_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCamelCase__    					=      ['''RemBertTokenizerFast''']

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCamelCase__    					=      [
      '''REMBERT_PRETRAINED_MODEL_ARCHIVE_LIST''',
      '''RemBertForCausalLM''',
      '''RemBertForMaskedLM''',
      '''RemBertForMultipleChoice''',
      '''RemBertForQuestionAnswering''',
      '''RemBertForSequenceClassification''',
      '''RemBertForTokenClassification''',
      '''RemBertLayer''',
      '''RemBertModel''',
      '''RemBertPreTrainedModel''',
      '''load_tf_weights_in_rembert''',
  ]


try:
  if not is_tf_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCamelCase__    					=      [
      '''TF_REMBERT_PRETRAINED_MODEL_ARCHIVE_LIST''',
      '''TFRemBertForCausalLM''',
      '''TFRemBertForMaskedLM''',
      '''TFRemBertForMultipleChoice''',
      '''TFRemBertForQuestionAnswering''',
      '''TFRemBertForSequenceClassification''',
      '''TFRemBertForTokenClassification''',
      '''TFRemBertLayer''',
      '''TFRemBertModel''',
      '''TFRemBertPreTrainedModel''',
  ]


if TYPE_CHECKING:
  from .configuration_rembert import REMBERT_PRETRAINED_CONFIG_ARCHIVE_MAP, RemBertConfig, RemBertOnnxConfig

  try:
    if not is_sentencepiece_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_rembert import RemBertTokenizer

  try:
    if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_rembert_fast import RemBertTokenizerFast

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_rembert import (
        REMBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
        RemBertForCausalLM,
        RemBertForMaskedLM,
        RemBertForMultipleChoice,
        RemBertForQuestionAnswering,
        RemBertForSequenceClassification,
        RemBertForTokenClassification,
        RemBertLayer,
        RemBertModel,
        RemBertPreTrainedModel,
        load_tf_weights_in_rembert,
    )

  try:
    if not is_tf_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_tf_rembert import (
        TF_REMBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
        TFRemBertForCausalLM,
        TFRemBertForMaskedLM,
        TFRemBertForMultipleChoice,
        TFRemBertForQuestionAnswering,
        TFRemBertForSequenceClassification,
        TFRemBertForTokenClassification,
        TFRemBertLayer,
        TFRemBertModel,
        TFRemBertPreTrainedModel,
    )


else:
  import sys

  UpperCamelCase__    					=      _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)
