




from __future__ import annotations

from collections.abc import Callable

UpperCamelCase__    			=			list[list[float | int]]







def 	_a      (						SCREAMING_SNAKE_CASE_							:				Matrix      ,      SCREAMING_SNAKE_CASE_							:				Matrix     ):
					__lowerCAmelCase				   =       len(SCREAMING_SNAKE_CASE_     )
					__lowerCAmelCase				   =       [[0 for _ in range(size + 1     )] for _ in range(SCREAMING_SNAKE_CASE_     )]
					__lowerCAmelCase				   =       42
					__lowerCAmelCase				   =       42
					__lowerCAmelCase				   =       42
					__lowerCAmelCase				   =       42
					__lowerCAmelCase				   =       42
					__lowerCAmelCase				   =       42

					for row in range(SCREAMING_SNAKE_CASE_     ):
										for col in range(SCREAMING_SNAKE_CASE_     ):
															__lowerCAmelCase				   =       matrix[row][col]

										__lowerCAmelCase				   =       vector[row][0]

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

										for rowa in range(row + 1      ,      SCREAMING_SNAKE_CASE_     ):
															__lowerCAmelCase				   =       augmented[rowa][col] / augmented[row][col]
															__lowerCAmelCase				   =       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      ,      SCREAMING_SNAKE_CASE_     ):
										for row in range(SCREAMING_SNAKE_CASE_     ):
															__lowerCAmelCase				   =       augmented[row][col] / augmented[col][col]
															for cola in range(SCREAMING_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(SCREAMING_SNAKE_CASE_     )
					]







def 	_a      (						SCREAMING_SNAKE_CASE_							:				list[int]     ):
					__lowerCAmelCase				   =       len(SCREAMING_SNAKE_CASE_     )
					__lowerCAmelCase				   =       [[0 for _ in range(SCREAMING_SNAKE_CASE_     )] for _ in range(SCREAMING_SNAKE_CASE_     )]
					__lowerCAmelCase				   =       [[0] for _ in range(SCREAMING_SNAKE_CASE_     )]
					__lowerCAmelCase				   =       42
					__lowerCAmelCase				   =       42
					__lowerCAmelCase				   =       42
					__lowerCAmelCase				   =       42

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

					__lowerCAmelCase				   =       solve(SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )

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

					return interpolated_func







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







def 	_a      (						SCREAMING_SNAKE_CASE_							:				Callable[[int], int] = question_function      ,      SCREAMING_SNAKE_CASE_							:				int = 10     ):
					__lowerCAmelCase				   =       [func(SCREAMING_SNAKE_CASE_     ) for x_val in range(1      ,      order + 1     )]

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

					__lowerCAmelCase				   =       0
					__lowerCAmelCase				   =       42
					__lowerCAmelCase				   =       42

					for poly in polynomials:
										__lowerCAmelCase				   =       1
										while func(SCREAMING_SNAKE_CASE_     ) == poly(SCREAMING_SNAKE_CASE_     ):
															x_val += 1

										ret += poly(SCREAMING_SNAKE_CASE_     )

					return ret


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










from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_speech_available, is_torch_available


UpperCamelCase__    			=			{
    """configuration_audio_spectrogram_transformer""": [
        """AUDIO_SPECTROGRAM_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """ASTConfig""",
    ]
}

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					UpperCamelCase__    			=			[
					    """AUDIO_SPECTROGRAM_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST""",
					    """ASTForAudioClassification""",
					    """ASTModel""",
					    """ASTPreTrainedModel""",
					]

try:
					if not is_speech_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					UpperCamelCase__    			=			["""ASTFeatureExtractor"""]

if TYPE_CHECKING:
					from .configuration_audio_spectrogram_transformer import (
					    AUDIO_SPECTROGRAM_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
					    ASTConfig,
					)

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_audio_spectrogram_transformer import (
										    AUDIO_SPECTROGRAM_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
										    ASTForAudioClassification,
										    ASTModel,
										    ASTPreTrainedModel,
										)

					try:
										if not is_speech_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .feature_extraction_audio_spectrogram_transformer import ASTFeatureExtractor


else:
					import sys

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




