

from __future__ import annotations

from collections.abc import Callable

A_			:					Optional[Any]    			=     list[list[float | int]]

def 		UpperCamelCase   (lowercase_:					Matrix       , lowercase_:					Matrix   )	-> int:
	A__				:       str	  =						len(__lowerCamelCase   )
	A__				:       Optional[int]	  =						[[0 for _ in range(size + 1   )] for _ in range(__lowerCamelCase   )]
	A__				:       Any	  =						42
	A__				:       Tuple	  =						42
	A__				:       List[Any]	  =						42
	A__				:       Dict	  =						42
	A__				:       Tuple	  =						42
	A__				:       Dict	  =						42

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

		A__				:       int	  =						vector[row][0]

	A__				:       int	  =						0
	A__				:       Dict	  =						0
	while row < size and col < size:
		# pivoting
		A__				:       Any	  =						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__				:       str	  =						augmented[pivot_row], augmented[row]

		for rowa in range(row + 1       , __lowerCamelCase   ):
			A__				:       Tuple	  =						augmented[rowa][col] / augmented[row][col]
			A__				:       Tuple	  =						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__				:       List[str]	  =						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 		UpperCamelCase   (lowercase_:					list[int]   )	-> Optional[Any]:
	A__				:       Optional[Any]	  =						len(__lowerCamelCase   )
	A__				:       Tuple	  =						[[0 for _ in range(__lowerCamelCase   )] for _ in range(__lowerCamelCase   )]
	A__				:       Optional[int]	  =						[[0] for _ in range(__lowerCamelCase   )]
	A__				:       List[str]	  =						42
	A__				:       Any	  =						42
	A__				:       Optional[int]	  =						42
	A__				:       Tuple	  =						42

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

	A__				:       Any	  =						solve(__lowerCamelCase       , __lowerCamelCase   )

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

	return interpolated_func

def 		UpperCamelCase   (lowercase_:					int   )	-> Optional[Any]:
	return (
	    1
	    - variable
	    + variable**2
	    - variable**3
	    + variable**4
	    - variable**5
	    + variable**6
	    - variable**7
	    + variable**8
	    - variable**9
	    + variable**10
	)

def 		UpperCamelCase   (lowercase_:					Callable[[int], int] = question_function       , lowercase_:					int = 10   )	-> str:
	A__				:       Tuple	  =						[func(__lowerCamelCase   ) for x_val in range(1       , order + 1   )]

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

	A__				:       List[Any]	  =						0
	A__				:       Tuple	  =						42
	A__				:       Dict	  =						42

	for poly in polynomials:
		A__				:       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_flax_available,
    is_tf_available,
    is_torch_available,
)


_lowercase          =						{"""configuration_vit_mae""": ["""VIT_MAE_PRETRAINED_CONFIG_ARCHIVE_MAP""", """ViTMAEConfig"""]}

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						_lowercase          =						[
						    """VIT_MAE_PRETRAINED_MODEL_ARCHIVE_LIST""",
						    """ViTMAEForPreTraining""",
						    """ViTMAELayer""",
						    """ViTMAEModel""",
						    """ViTMAEPreTrainedModel""",
						]

try:
						if not is_tf_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						_lowercase          =						[
						    """TFViTMAEForPreTraining""",
						    """TFViTMAEModel""",
						    """TFViTMAEPreTrainedModel""",
						]

if TYPE_CHECKING:
						from .configuration_vit_mae import VIT_MAE_PRETRAINED_CONFIG_ARCHIVE_MAP, ViTMAEConfig

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_vit_mae import (
												    VIT_MAE_PRETRAINED_MODEL_ARCHIVE_LIST,
												    ViTMAEForPreTraining,
												    ViTMAELayer,
												    ViTMAEModel,
												    ViTMAEPreTrainedModel,
												)

						try:
												if not is_tf_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_tf_vit_mae import TFViTMAEForPreTraining, TFViTMAEModel, TFViTMAEPreTrainedModel


else:
						import sys

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