




'''simple docstring'''





from __future__ import annotations

from collections.abc import Callable

_SCREAMING_SNAKE_CASE							:       List[str]						=			list[list[float | int]]


def 					UpperCamelCase_(     snake_case							:	Matrix							,    snake_case							:	Matrix					):

							'''simple docstring'''






							snake_case_      =				len(snake_case					)
							snake_case_      =				[[0 for _ in range(size + 1					)] for _ in range(snake_case					)]
							snake_case_      =				42
							snake_case_      =				42
							snake_case_      =				42
							snake_case_      =				42
							snake_case_      =				42
							snake_case_      =				42

							for row in range(snake_case					):
														for col in range(snake_case					):
																					snake_case_      =				matrix[row][col]

														snake_case_      =				vector[row][0]

							snake_case_      =				0
							snake_case_      =				0
							while row < size and col < size:
														# pivoting
														snake_case_      =				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:
																					snake_case_ ,				snake_case_      =				augmented[pivot_row], augmented[row]

														for rowa in range(row + 1							,    snake_case					):
																					snake_case_      =				augmented[rowa][col] / augmented[row][col]
																					snake_case_      =				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					):
																					snake_case_      =				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]							,    1_0					)] for row in range(snake_case					)
							]


def 					UpperCamelCase_(     snake_case							:	list[int]					):

							'''simple docstring'''






							snake_case_      =				len(snake_case					)
							snake_case_      =				[[0 for _ in range(snake_case					)] for _ in range(snake_case					)]
							snake_case_      =				[[0] for _ in range(snake_case					)]
							snake_case_      =				42
							snake_case_      =				42
							snake_case_      =				42
							snake_case_      =				42

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

							snake_case_      =				solve(snake_case							,    snake_case					)

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

							return interpolated_func


def 					UpperCamelCase_(     snake_case							:	int					):

							'''simple docstring'''






							return (
							    1
							    - variable
							    + variable**2
							    - variable**3
							    + variable**4
							    - variable**5
							    + variable**6
							    - variable**7
							    + variable**8
							    - variable**9
							    + variable**1_0
							)


def 					UpperCamelCase_(     snake_case							:	Callable[[int], int] = question_function							,    snake_case							:	int = 1_0					):

							'''simple docstring'''






							snake_case_      =				[func(snake_case					) for x_val in range(1							,    order + 1					)]

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

							snake_case_      =				0
							snake_case_      =				42
							snake_case_      =				42

							for poly in polynomials:
														snake_case_      =				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 typing import TYPE_CHECKING

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


_SCREAMING_SNAKE_CASE							:       Optional[int]						=			{
    "configuration_canine": ["CANINE_PRETRAINED_CONFIG_ARCHIVE_MAP", "CanineConfig"],
    "tokenization_canine": ["CanineTokenizer"],
}

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		_SCREAMING_SNAKE_CASE							:       Dict						=			[
		    "CANINE_PRETRAINED_MODEL_ARCHIVE_LIST",
		    "CanineForMultipleChoice",
		    "CanineForQuestionAnswering",
		    "CanineForSequenceClassification",
		    "CanineForTokenClassification",
		    "CanineLayer",
		    "CanineModel",
		    "CaninePreTrainedModel",
		    "load_tf_weights_in_canine",
		]


if TYPE_CHECKING:
		from .configuration_canine import CANINE_PRETRAINED_CONFIG_ARCHIVE_MAP, CanineConfig
		from .tokenization_canine import CanineTokenizer

		try:
				if not is_torch_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_canine import (
				    CANINE_PRETRAINED_MODEL_ARCHIVE_LIST,
				    CanineForMultipleChoice,
				    CanineForQuestionAnswering,
				    CanineForSequenceClassification,
				    CanineForTokenClassification,
				    CanineLayer,
				    CanineModel,
				    CaninePreTrainedModel,
				    load_tf_weights_in_canine,
				)


else:
		import sys

		_SCREAMING_SNAKE_CASE							:       int						=			_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)




