






'''simple docstring'''

from __future__ import annotations

from collections.abc import Callable

UpperCAmelCase__						:Union[str, Any]          =			list[list[float | int]]
def     __lowercase  (_lowercase,						_lowercase     )   ->     Union[str, Any]:


     """simple docstring"""
     __lowerCamelCase						:       int				   =				len(snake_case_     )
     __lowerCamelCase						:       Matrix				   =				[[0 for _ in range(size + 1     )] for _ in range(snake_case_     )]
     __lowerCamelCase						:       int
     __lowerCamelCase						:       int
     __lowerCamelCase						:       int
     __lowerCamelCase						:       int
     __lowerCamelCase						:       int
     __lowerCamelCase						:       float

     for row in range(snake_case_     ):
          for col in range(snake_case_     ):
               __lowerCamelCase						:       Union[str, Any]				   =				matrix[row][col]

          __lowerCamelCase						:       Any				   =				vector[row][0]

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

          for rowa in range(row + 1,						snake_case_     ):
               __lowerCamelCase						:       Dict				   =				augmented[rowa][col] / augmented[row][col]
               __lowerCamelCase						:       Optional[Any]				   =				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,						snake_case_     ):
          for row in range(snake_case_     ):
               __lowerCamelCase						:       Any				   =				augmented[row][col] / augmented[col][col]
               for cola in range(snake_case_,						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(snake_case_     )
     ]
def     __lowercase  (_lowercase     )   ->     Optional[Any]:


     """simple docstring"""
     __lowerCamelCase						:       int				   =				len(snake_case_     )
     __lowerCamelCase						:       Matrix				   =				[[0 for _ in range(snake_case_     )] for _ in range(snake_case_     )]
     __lowerCamelCase						:       Matrix				   =				[[0] for _ in range(snake_case_     )]
     __lowerCamelCase						:       Matrix
     __lowerCamelCase						:       int
     __lowerCamelCase						:       int
     __lowerCamelCase						:       int

     for x_val, y_val in enumerate(snake_case_     ):
          for col in range(snake_case_     ):
               __lowerCamelCase						:       Tuple				   =				(x_val + 1) ** (size - col - 1)
          __lowerCamelCase						:       Tuple				   =				y_val

     __lowerCamelCase						:       Any				   =				solve(snake_case_,						snake_case_     )

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

     return interpolated_func
def     __lowercase  (_lowercase     )   ->     str:


     """simple docstring"""
     return (
         1
         - variable
         + variable**2
         - variable**3
         + variable**4
         - variable**5
         + variable**6
         - variable**7
         + variable**8
         - variable**9
         + variable**10
     )
def     __lowercase  (_lowercase = question_function,						_lowercase = 10     )   ->     List[Any]:


     """simple docstring"""
     __lowerCamelCase						:       list[int]				   =				[func(snake_case_     ) for x_val in range(1,						order + 1     )]

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

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

     for poly in polynomials:
          __lowerCamelCase						:       Tuple				   =				1
          while func(snake_case_     ) == poly(snake_case_     ):
               x_val += 1

          ret += poly(snake_case_     )

     return ret


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











'''simple docstring'''

from ...processing_utils import ProcessorMixin







class 	SCREAMING_SNAKE_CASE	(      lowerCAmelCase_  ):
       snake_case__    :     List[Any]   		=			'SpeechT5FeatureExtractor'
       snake_case__    :     Union[str, Any]   		=			'SpeechT5Tokenizer'




       def __init__(					self      : Union[str, Any]	,    A__      : str	,    A__      : Tuple					):


            """simple docstring"""







            super().__init__(A__	,    A__					)




       def __call__(					self      : List[Any]	,    *A__      : Any	,    **A__      : Optional[int]					):


            """simple docstring"""







            __lowerCamelCase						:       Any				   =				kwargs.pop("""audio"""	,    A__					)
            __lowerCamelCase						:       Any				   =				kwargs.pop("""text"""	,    A__					)
            __lowerCamelCase						:       Union[str, Any]				   =				kwargs.pop("""text_target"""	,    A__					)
            __lowerCamelCase						:       Union[str, Any]				   =				kwargs.pop("""audio_target"""	,    A__					)
            __lowerCamelCase						:       Any				   =				kwargs.pop("""sampling_rate"""	,    A__					)

            if audio is not None and text is not None:
                 raise ValueError(
                     """Cannot process both `audio` and `text` inputs. Did you mean `audio_target` or `text_target`?"""					)
            if audio_target is not None and text_target is not None:
                 raise ValueError(
                     """Cannot process both `audio_target` and `text_target` inputs. Did you mean `audio` or `text`?"""					)
            if audio is None and audio_target is None and text is None and text_target is None:
                 raise ValueError(
                     """You need to specify either an `audio`, `audio_target`, `text`, or `text_target` input to process."""					)

            if audio is not None:
                 __lowerCamelCase						:       Optional[int]				   =				self.feature_extractor(A__	,    *A__	,    sampling_rate=A__	,    **A__					)
            elif text is not None:
                 __lowerCamelCase						:       Optional[int]				   =				self.tokenizer(A__	,    **A__					)
            else:
                 __lowerCamelCase						:       Tuple				   =				None

            if audio_target is not None:
                 __lowerCamelCase						:       Optional[int]				   =				self.feature_extractor(audio_target=A__	,    *A__	,    sampling_rate=A__	,    **A__					)
                 __lowerCamelCase						:       Union[str, Any]				   =				targets["""input_values"""]
            elif text_target is not None:
                 __lowerCamelCase						:       Tuple				   =				self.tokenizer(A__	,    **A__					)
                 __lowerCamelCase						:       List[str]				   =				targets["""input_ids"""]
            else:
                 __lowerCamelCase						:       Dict				   =				None

            if inputs is None:
                 return targets

            if targets is not None:
                 __lowerCamelCase						:       str				   =				labels

                 __lowerCamelCase						:       int				   =				targets.get("""attention_mask"""					)
                 if decoder_attention_mask is not None:
                      __lowerCamelCase						:       Optional[int]				   =				decoder_attention_mask

            return inputs




       def 					a_					(					self      : Any	,    *A__      : Union[str, Any]	,    **A__      : List[str]					):


            """simple docstring"""







            __lowerCamelCase						:       Optional[int]				   =				kwargs.pop("""input_values"""	,    A__					)
            __lowerCamelCase						:       List[Any]				   =				kwargs.pop("""input_ids"""	,    A__					)
            __lowerCamelCase						:       List[Any]				   =				kwargs.pop("""labels"""	,    A__					)

            if input_values is not None and input_ids is not None:
                 raise ValueError("""Cannot process both `input_values` and `input_ids` inputs."""					)
            if input_values is None and input_ids is None and labels is None:
                 raise ValueError(
                     """You need to specify either an `input_values`, `input_ids`, or `labels` input to be padded."""					)

            if input_values is not None:
                 __lowerCamelCase						:       List[Any]				   =				self.feature_extractor.pad(A__	,    *A__	,    **A__					)
            elif input_ids is not None:
                 __lowerCamelCase						:       Any				   =				self.tokenizer.pad(A__	,    **A__					)
            else:
                 __lowerCamelCase						:       Any				   =				None

            if labels is not None:
                 if "input_ids" in labels or (isinstance(A__	,    A__					) and "input_ids" in labels[0]):
                      __lowerCamelCase						:       List[Any]				   =				self.tokenizer.pad(A__	,    **A__					)
                      __lowerCamelCase						:       Tuple				   =				targets["""input_ids"""]
                 else:
                      __lowerCamelCase						:       Optional[int]				   =				self.feature_extractor.feature_size
                      __lowerCamelCase						:       Any				   =				self.feature_extractor.num_mel_bins
                      __lowerCamelCase						:       List[str]				   =				self.feature_extractor.pad(A__	,    *A__	,    **A__					)
                      __lowerCamelCase						:       Dict				   =				feature_size_hack
                      __lowerCamelCase						:       List[Any]				   =				targets["""input_values"""]
            else:
                 __lowerCamelCase						:       Optional[int]				   =				None

            if inputs is None:
                 return targets

            if targets is not None:
                 __lowerCamelCase						:       Dict				   =				labels

                 __lowerCamelCase						:       List[str]				   =				targets.get("""attention_mask"""					)
                 if decoder_attention_mask is not None:
                      __lowerCamelCase						:       int				   =				decoder_attention_mask

            return inputs




       def 					a_					(					self      : Optional[Any]	,    *A__      : List[Any]	,    **A__      : Optional[int]					):


            """simple docstring"""







            return self.tokenizer.batch_decode(*A__	,    **A__					)




       def 					a_					(					self      : Any	,    *A__      : int	,    **A__      : Dict					):


            """simple docstring"""







            return self.tokenizer.decode(*A__	,    **A__					)



