



'''simple docstring'''



from __future__ import annotations

from collections.abc import Callable

lowerCAmelCase_     :       Optional[Any]								=						list[list[float | int]]
def 					UpperCAmelCase   (						A  :				Matrix					,		A  :				Matrix				):
							SCREAMING_SNAKE_CASE					:      int     					=			len(A				)
							SCREAMING_SNAKE_CASE					:      Matrix     					=			[[0 for _ in range(size + 1				)] for _ in range(A				)]
							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(A				):
														for col in range(A				):
																					SCREAMING_SNAKE_CASE					:      Optional[int]     					=			matrix[row][col]

														SCREAMING_SNAKE_CASE					:      Optional[Any]     					=			vector[row][0]

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

														for rowa in range(row + 1					,		A				):
																					SCREAMING_SNAKE_CASE					:      Dict     					=			augmented[rowa][col] / augmented[row][col]
																					SCREAMING_SNAKE_CASE					:      Union[str, Any]     					=			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					,		A				):
														for row in range(A				):
																					SCREAMING_SNAKE_CASE					:      int     					=			augmented[row][col] / augmented[col][col]
																					for cola in range(A					,		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(A				)
							]
def 					UpperCAmelCase   (						A  :				list[int]				):
							SCREAMING_SNAKE_CASE					:      int     					=			len(A				)
							SCREAMING_SNAKE_CASE					:      Matrix     					=			[[0 for _ in range(A				)] for _ in range(A				)]
							SCREAMING_SNAKE_CASE					:      Matrix     					=			[[0] for _ in range(A				)]
							SCREAMING_SNAKE_CASE					:      Matrix
							SCREAMING_SNAKE_CASE					:      int
							SCREAMING_SNAKE_CASE					:      int
							SCREAMING_SNAKE_CASE					:      int

							for x_val, y_val in enumerate(A				):
														for col in range(A				):
																					SCREAMING_SNAKE_CASE					:      List[str]     					=			(x_val + 1) ** (size - col - 1)
														SCREAMING_SNAKE_CASE					:      Tuple     					=			y_val

							SCREAMING_SNAKE_CASE					:      Optional[Any]     					=			solve(A					,		A				)

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

							return interpolated_func
def 					UpperCAmelCase   (						A  :				int				):
							return (
							    1
							    - variable
							    + variable**2
							    - variable**3
							    + variable**4
							    - variable**5
							    + variable**6
							    - variable**7
							    + variable**8
							    - variable**9
							    + variable**10
							)
def 					UpperCAmelCase   (						A  :				Callable[[int], int] = question_function					,		A  :				int = 10				):
							SCREAMING_SNAKE_CASE					:      list[int]     					=			[func(A				) 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					:      Tuple     					=			1
														while func(A				) == poly(A				):
																					x_val += 1

														ret += poly(A				)

							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




