

from __future__ import annotations

from collections.abc import Callable

a_      =     list[list[float | int]]

def 			lowerCamelCase__			(       _a				,      _a):
	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 :   List[Any]					  =							matrix[row][col]

		SCREAMING_SNAKE_CASE :   int					  =							vector[row][0]

	SCREAMING_SNAKE_CASE :   Optional[Any]					  =							0
	SCREAMING_SNAKE_CASE :   List[str]					  =							0
	while row < size and col < size:
		# pivoting
		SCREAMING_SNAKE_CASE :   List[str]					  =							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 :   int					  =							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 :   List[Any]					  =							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 			lowerCamelCase__			(       _a):
	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 :   Any					  =							(x_val + 1) ** (size - col - 1)
		SCREAMING_SNAKE_CASE :   Tuple					  =							y_val

	SCREAMING_SNAKE_CASE :   Any					  =							solve(_a				,      _a)

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

	return interpolated_func

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

def 			lowerCamelCase__			(       _a = question_function				,      _a = 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 :   Union[str, Any]					  =							1
		while func(_a) == poly(_a):
			x_val += 1

		ret += poly(_a)

	return ret


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


a_      =     frozenset(
    [
        'prompt',
        'height',
        'width',
        'guidance_scale',
        'negative_prompt',
        'prompt_embeds',
        'negative_prompt_embeds',
        'cross_attention_kwargs',
    ]
)

a_      =     frozenset(['prompt', 'negative_prompt'])

a_      =     frozenset([])

a_      =     frozenset(['image'])

a_      =     frozenset(
    [
        'image',
        'height',
        'width',
        'guidance_scale',
    ]
)

a_      =     frozenset(['image'])

a_      =     frozenset(
    [
        'prompt',
        'image',
        'height',
        'width',
        'guidance_scale',
        'negative_prompt',
        'prompt_embeds',
        'negative_prompt_embeds',
    ]
)

a_      =     frozenset(['prompt', 'image', 'negative_prompt'])

a_      =     frozenset(
    [
        # Text guided image variation with an image mask
        'prompt',
        'image',
        'mask_image',
        'height',
        'width',
        'guidance_scale',
        'negative_prompt',
        'prompt_embeds',
        'negative_prompt_embeds',
    ]
)

a_      =     frozenset(['prompt', 'image', 'mask_image', 'negative_prompt'])

a_      =     frozenset(
    [
        # image variation with an image mask
        'image',
        'mask_image',
        'height',
        'width',
        'guidance_scale',
    ]
)

a_      =     frozenset(['image', 'mask_image'])

a_      =     frozenset(
    [
        'example_image',
        'image',
        'mask_image',
        'height',
        'width',
        'guidance_scale',
    ]
)

a_      =     frozenset(['example_image', 'image', 'mask_image'])

a_      =     frozenset(['class_labels'])

a_      =     frozenset(['class_labels'])

a_      =     frozenset(['batch_size'])

a_      =     frozenset([])

a_      =     frozenset(['batch_size'])

a_      =     frozenset([])

a_      =     frozenset(
    [
        'prompt',
        'audio_length_in_s',
        'guidance_scale',
        'negative_prompt',
        'prompt_embeds',
        'negative_prompt_embeds',
        'cross_attention_kwargs',
    ]
)

a_      =     frozenset(['prompt', 'negative_prompt'])
a_      =     frozenset(['input_tokens'])

a_      =     frozenset(['input_tokens'])