
"""simple docstring"""




from __future__ import annotations

from collections.abc import Callable

a		:       int     						=       list[list[float | int]]



def     __magic_name__		(					UpperCamelCase     :		Matrix							,		UpperCamelCase     :		Matrix     )     ->						Matrix:
    a__		=			len(UpperCamelCase     )
    a__		=			[[0 for _ in range(size + 1     )] for _ in range(UpperCamelCase     )]
    a__		=			42
    a__		=			42
    a__		=			42
    a__		=			42
    a__		=			42
    a__		=			42

    for row in range(UpperCamelCase     ):
        for col in range(UpperCamelCase     ):
            a__		=			matrix[row][col]

        a__		=			vector[row][0]

    a__		=			0
    a__		=			0
    while row < size and col < size:
        # pivoting
        a__		=			max((abs(augmented[rowa][col]     ), rowa) for rowa in range(UpperCamelCase							,		UpperCamelCase     )     )[
            1
        ]
        if augmented[pivot_row][col] == 0:
            col += 1
            continue
        else:
            a__	,     a__		=			augmented[pivot_row], augmented[row]

        for rowa in range(row + 1							,		UpperCamelCase     ):
            a__		=			augmented[rowa][col] / augmented[row][col]
            a__		=			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							,		UpperCamelCase     ):
        for row in range(UpperCamelCase     ):
            a__		=			augmented[row][col] / augmented[col][col]
            for cola in range(UpperCamelCase							,		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(UpperCamelCase     )
    ]



def     __magic_name__		(					UpperCamelCase     :		list[int]     )     ->						Callable[[int], int]:
    a__		=			len(UpperCamelCase     )
    a__		=			[[0 for _ in range(UpperCamelCase     )] for _ in range(UpperCamelCase     )]
    a__		=			[[0] for _ in range(UpperCamelCase     )]
    a__		=			42
    a__		=			42
    a__		=			42
    a__		=			42

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

    a__		=			solve(UpperCamelCase							,		UpperCamelCase     )

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

    return interpolated_func



def     __magic_name__		(					UpperCamelCase     :		int     )     ->						int:
    return (
        1
        - variable
        + variable**2
        - variable**3
        + variable**4
        - variable**5
        + variable**6
        - variable**7
        + variable**8
        - variable**9
        + variable**10
    )



def     __magic_name__		(					UpperCamelCase     :		Callable[[int], int] = question_function							,		UpperCamelCase     :		int = 10     )     ->						int:
    a__		=			[func(UpperCamelCase     ) for x_val in range(1							,		order + 1     )]

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

    a__		=			0
    a__		=			42
    a__		=			42

    for poly in polynomials:
        a__		=			1
        while func(UpperCamelCase     ) == poly(UpperCamelCase     ):
            x_val += 1

        ret += poly(UpperCamelCase     )

    return ret


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




"""simple docstring"""




import random
import unittest

import torch

from diffusers import IFImgaImgSuperResolutionPipeline
from diffusers.utils import floats_tensor
from diffusers.utils.import_utils import is_xformers_available
from diffusers.utils.testing_utils import skip_mps, torch_device

from ..pipeline_params import TEXT_GUIDED_IMAGE_VARIATION_BATCH_PARAMS, TEXT_GUIDED_IMAGE_VARIATION_PARAMS
from ..test_pipelines_common import PipelineTesterMixin
from . import IFPipelineTesterMixin







@skip_mps
class     lowercase(_lowercase    ,						_lowercase    ,						unittest.TestCase       ):
     __snake_case:	Optional[int]						=     IFImgaImgSuperResolutionPipeline
     __snake_case:	Dict						=     TEXT_GUIDED_IMAGE_VARIATION_PARAMS - {'width', 'height'}
     __snake_case:	Any						=     TEXT_GUIDED_IMAGE_VARIATION_BATCH_PARAMS.union({'original_image'}       )
     __snake_case:	List[Any]						=     PipelineTesterMixin.required_optional_params - {'latents'}



     def 			lowercase__  (							self   )		->     Tuple:







         """simple docstring"""



         return self._get_superresolution_dummy_components()



     def 			lowercase__  (							self     ,				__SCREAMING_SNAKE_CASE     ,				__SCREAMING_SNAKE_CASE=0   )		->     Union[str, Any]:







         """simple docstring"""



         if str(__SCREAMING_SNAKE_CASE   ).startswith('mps'   ):
             a__		=			torch.manual_seed(__SCREAMING_SNAKE_CASE   )
         else:
             a__		=			torch.Generator(device=__SCREAMING_SNAKE_CASE   ).manual_seed(__SCREAMING_SNAKE_CASE   )

         a__		=			floats_tensor((1, 3, 3_2, 3_2)     ,				rng=random.Random(__SCREAMING_SNAKE_CASE   )   ).to(__SCREAMING_SNAKE_CASE   )
         a__		=			floats_tensor((1, 3, 1_6, 1_6)     ,				rng=random.Random(__SCREAMING_SNAKE_CASE   )   ).to(__SCREAMING_SNAKE_CASE   )

         a__		=			{
             'prompt': 'A painting of a squirrel eating a burger',
             'image': image,
             'original_image': original_image,
             'generator': generator,
             'num_inference_steps': 2,
             'output_type': 'numpy',
         }

         return inputs



     @unittest.skipIf(
         torch_device != 'cuda' or not is_xformers_available()     ,				reason='XFormers attention is only available with CUDA and `xformers` installed'     ,				)
     def 			lowercase__  (							self   )		->     Optional[int]:







         """simple docstring"""



         self._test_xformers_attention_forwardGenerator_pass(expected_max_diff=1e-3   )



     def 			lowercase__  (							self   )		->     Any:







         """simple docstring"""



         self._test_save_load_optional_components()



     @unittest.skipIf(torch_device != 'cuda'     ,				reason='float16 requires CUDA'   )
     def 			lowercase__  (							self   )		->     List[Any]:







         """simple docstring"""



         super().test_save_load_floataa(expected_max_diff=1e-1   )



     def 			lowercase__  (							self   )		->     List[str]:







         """simple docstring"""



         self._test_attention_slicing_forward_pass(expected_max_diff=1e-2   )



     def 			lowercase__  (							self   )		->     Optional[Any]:







         """simple docstring"""



         self._test_save_load_local()




     def 			lowercase__  (							self   )		->     Any:







         """simple docstring"""



         self._test_inference_batch_single_identical(
             expected_max_diff=1e-2     ,				)


