
'''simple docstring'''



from __future__ import annotations

from collections.abc import Callable

_lowercase          =						list[list[float | int]]


def A (__lowerCamelCase :Matrix					,      __lowerCamelCase :Matrix						):
						_lowerCAmelCase    		=					len(__lowerCamelCase						)
						_lowerCAmelCase    		=					[[0 for _ in range(size + 1						)] for _ in range(__lowerCamelCase						)]
						_lowerCAmelCase    		=					42
						_lowerCAmelCase    		=					42
						_lowerCAmelCase    		=					42
						_lowerCAmelCase    		=					42
						_lowerCAmelCase    		=					42
						_lowerCAmelCase    		=					42

						for row in range(__lowerCamelCase						):
												for col in range(__lowerCamelCase						):
																		_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(__lowerCamelCase					,      __lowerCamelCase						)						)[
												    1
												]
												if augmented[pivot_row][col] == 0:
																		col += 1
																		continue
												else:
																		_lowerCAmelCase		,       _lowerCAmelCase    		=					augmented[pivot_row], augmented[row]

												for rowa in range(row + 1					,      __lowerCamelCase						):
																		_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					,      __lowerCamelCase						):
												for row in range(__lowerCamelCase						):
																		_lowerCAmelCase    		=					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 A (__lowerCamelCase :list[int]						):
						_lowerCAmelCase    		=					len(__lowerCamelCase						)
						_lowerCAmelCase    		=					[[0 for _ in range(__lowerCamelCase						)] for _ in range(__lowerCamelCase						)]
						_lowerCAmelCase    		=					[[0] for _ in range(__lowerCamelCase						)]
						_lowerCAmelCase    		=					42
						_lowerCAmelCase    		=					42
						_lowerCAmelCase    		=					42
						_lowerCAmelCase    		=					42

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

						_lowerCAmelCase    		=					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 A (__lowerCamelCase :int						):
						return (
						    1
						    - variable
						    + variable**2
						    - variable**3
						    + variable**4
						    - variable**5
						    + variable**6
						    - variable**7
						    + variable**8
						    - variable**9
						    + variable**10
						)


def A (__lowerCamelCase :Callable[[int], int] = question_function					,      __lowerCamelCase :int = 10						):
						_lowerCAmelCase    		=					[func(__lowerCamelCase						) 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(__lowerCamelCase						) == poly(__lowerCamelCase						):
																		x_val += 1

												ret += poly(__lowerCamelCase						)

						return ret


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


'''simple docstring'''



from ...utils import (
    OptionalDependencyNotAvailable,
    is_torch_available,
    is_transformers_available,
    is_transformers_version,
)


try:
						if not (is_transformers_available() and is_torch_available()):
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						from ...utils.dummy_torch_and_transformers_objects import (
						    ImageTextPipelineOutput,
						    UniDiffuserPipeline,
						)
else:
						from .modeling_text_decoder import UniDiffuserTextDecoder
						from .modeling_uvit import UniDiffuserModel, UTransformeraDModel
						from .pipeline_unidiffuser import ImageTextPipelineOutput, UniDiffuserPipeline
