



'''simple docstring'''




from __future__ import annotations

from collections.abc import Callable

UpperCamelCase__ :			Dict												=				list[list[float | int]]


def        lowerCAmelCase_     (			_lowerCamelCase:     Matrix ,   _lowerCamelCase:     Matrix      ):
		__SCREAMING_SNAKE_CASE :	int					 =	len(_lowerCamelCase      )
		__SCREAMING_SNAKE_CASE :	Matrix					 =	[[0 for _ in range(size + 1      )] for _ in range(_lowerCamelCase      )]
		__SCREAMING_SNAKE_CASE :	int
		__SCREAMING_SNAKE_CASE :	int
		__SCREAMING_SNAKE_CASE :	int
		__SCREAMING_SNAKE_CASE :	int
		__SCREAMING_SNAKE_CASE :	int
		__SCREAMING_SNAKE_CASE :	float

		for row in range(_lowerCamelCase      ):
				for col in range(_lowerCamelCase      ):
						__SCREAMING_SNAKE_CASE :	int					 =	matrix[row][col]

				__SCREAMING_SNAKE_CASE :	Union[str, Any]					 =	vector[row][0]

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

				for rowa in range(row + 1 ,   _lowerCamelCase      ):
						__SCREAMING_SNAKE_CASE :	int					 =	augmented[rowa][col] / augmented[row][col]
						__SCREAMING_SNAKE_CASE :	List[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      ):
						__SCREAMING_SNAKE_CASE :	Tuple					 =	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        lowerCAmelCase_     (			_lowerCamelCase:     list[int]      ):
		__SCREAMING_SNAKE_CASE :	int					 =	len(_lowerCamelCase      )
		__SCREAMING_SNAKE_CASE :	Matrix					 =	[[0 for _ in range(_lowerCamelCase      )] for _ in range(_lowerCamelCase      )]
		__SCREAMING_SNAKE_CASE :	Matrix					 =	[[0] for _ in range(_lowerCamelCase      )]
		__SCREAMING_SNAKE_CASE :	Matrix
		__SCREAMING_SNAKE_CASE :	int
		__SCREAMING_SNAKE_CASE :	int
		__SCREAMING_SNAKE_CASE :	int

		for x_val, y_val in enumerate(_lowerCamelCase      ):
				for col in range(_lowerCamelCase      ):
						__SCREAMING_SNAKE_CASE :	Any					 =	(x_val + 1) ** (size - col - 1)
				__SCREAMING_SNAKE_CASE :	int					 =	y_val

		__SCREAMING_SNAKE_CASE :	Tuple					 =	solve(_lowerCamelCase ,   _lowerCamelCase      )

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

		return interpolated_func


def        lowerCAmelCase_     (			_lowerCamelCase:     int      ):
		return (
		    1
		    - variable
		    + variable**2
		    - variable**3
		    + variable**4
		    - variable**5
		    + variable**6
		    - variable**7
		    + variable**8
		    - variable**9
		    + variable**10
		)


def        lowerCAmelCase_     (			_lowerCamelCase:     Callable[[int], int] = question_function ,   _lowerCamelCase:     int = 10      ):
		__SCREAMING_SNAKE_CASE :	list[int]					 =	[func(_lowerCamelCase      ) for x_val in range(1 ,   order + 1      )]

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

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

		for poly in polynomials:
				__SCREAMING_SNAKE_CASE :	List[Any]					 =	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_torch_available


UpperCamelCase__ :			Optional[int]												=				{'''configuration_wavlm''': ['''WAVLM_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''WavLMConfig''']}

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						UpperCamelCase__ :			Tuple												=				[
						    '''WAVLM_PRETRAINED_MODEL_ARCHIVE_LIST''',
						    '''WavLMForAudioFrameClassification''',
						    '''WavLMForCTC''',
						    '''WavLMForSequenceClassification''',
						    '''WavLMForXVector''',
						    '''WavLMModel''',
						    '''WavLMPreTrainedModel''',
						]

if TYPE_CHECKING:
						from .configuration_wavlm import WAVLM_PRETRAINED_CONFIG_ARCHIVE_MAP, WavLMConfig

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_wavlm import (
												    WAVLM_PRETRAINED_MODEL_ARCHIVE_LIST,
												    WavLMForAudioFrameClassification,
												    WavLMForCTC,
												    WavLMForSequenceClassification,
												    WavLMForXVector,
												    WavLMModel,
												    WavLMPreTrainedModel,
												)

else:
						import sys

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