
from __future__ import annotations

from collections.abc import Callable

__lowerCAmelCase					:			Tuple			      =		list[list[float | int]]


def     UpperCAmelCase_  (						__lowerCAmelCase	,					__lowerCAmelCase	) ->						Matrix:
    __lowercase		:			int	    =       len(__lowerCAmelCase	)
    __lowercase		:			Matrix	    =       [[0 for _ in range(size + 1	)] for _ in range(__lowerCAmelCase	)]
    __lowercase		:			int
    __lowercase		:			int
    __lowercase		:			int
    __lowercase		:			int
    __lowercase		:			int
    __lowercase		:			float

    for row in range(__lowerCAmelCase	):
        for col in range(__lowerCAmelCase	):
            __lowercase		:			Optional[Any]	    =       matrix[row][col]

        __lowercase		:			Dict	    =       vector[row][0]

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

        for rowa in range(row + 1	,					__lowerCAmelCase	):
            __lowercase		:			Union[str, Any]	    =       augmented[rowa][col] / augmented[row][col]
            __lowercase		:			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	,					__lowerCAmelCase	):
        for row in range(__lowerCAmelCase	):
            __lowercase		:			int	    =       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     UpperCAmelCase_  (						__lowerCAmelCase	) ->						Callable[[int], int]:
    __lowercase		:			int	    =       len(__lowerCAmelCase	)
    __lowercase		:			Matrix	    =       [[0 for _ in range(__lowerCAmelCase	)] for _ in range(__lowerCAmelCase	)]
    __lowercase		:			Matrix	    =       [[0] for _ in range(__lowerCAmelCase	)]
    __lowercase		:			Matrix
    __lowercase		:			int
    __lowercase		:			int
    __lowercase		:			int

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

    __lowercase		:			Any	    =       solve(__lowerCAmelCase	,					__lowerCAmelCase	)

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

    return interpolated_func


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


def     UpperCAmelCase_  (						__lowerCAmelCase = question_function	,					__lowerCAmelCase = 10	) ->						int:
    __lowercase		:			list[int]	    =       [func(__lowerCAmelCase	) for x_val in range(1	,					order + 1	)]

    __lowercase		:			list[Callable[[int], int]]	    =       [
        interpolate(data_points[:max_coeff]	) for max_coeff in range(1	,					order + 1	)
    ]

    __lowercase		:			int	    =       0
    __lowercase		:			Callable[[int], int]
    __lowercase		:			int

    for poly in polynomials:
        __lowercase		:			Optional[int]	    =       1
        while func(__lowerCAmelCase	) == poly(__lowerCAmelCase	):
            x_val += 1

        ret += poly(__lowerCAmelCase	)

    return ret


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




import unittest

import numpy as np

from diffusers import OnnxStableDiffusionInpaintPipelineLegacy
from diffusers.utils.testing_utils import (
    is_onnx_available,
    load_image,
    load_numpy,
    nightly,
    require_onnxruntime,
    require_torch_gpu,
)


if is_onnx_available():
 import onnxruntime as ort


@nightly
@require_onnxruntime
@require_torch_gpu
class 						__lowerCAmelCase	(	unittest.TestCase      ):



      """simple docstring"""







      @property
      def 		snake_case_			(      self		:       Union[str, Any]				):
          return (
              "CUDAExecutionProvider",
              {
                  "gpu_mem_limit": "15000000000",  # 15GB
                  "arena_extend_strategy": "kSameAsRequested",
              },
          )




      @property
      def 		snake_case_			(      self		:       Optional[Any]				):
          __lowercase		:			Tuple	    =       ort.SessionOptions()
          __lowercase		:			List[Any]	    =       False
          return options




      def 		snake_case_			(      self		:       Dict				):
          __lowercase		:			int	    =       load_image(
              '''https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main'''
              '''/in_paint/overture-creations-5sI6fQgYIuo.png'''				)
          __lowercase		:			int	    =       load_image(
              '''https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main'''
              '''/in_paint/overture-creations-5sI6fQgYIuo_mask.png'''				)
          __lowercase		:			Optional[Any]	    =       load_numpy(
              '''https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main'''
              '''/in_paint/red_cat_sitting_on_a_park_bench_onnx.npy'''				)

          # using the PNDM scheduler by default
          __lowercase		:			Union[str, Any]	    =       OnnxStableDiffusionInpaintPipelineLegacy.from_pretrained(
              '''CompVis/stable-diffusion-v1-4'''				,       revision='''onnx'''				,       safety_checker=_snake_case				,       feature_extractor=_snake_case				,       provider=self.gpu_provider				,       sess_options=self.gpu_options				,       )
          pipe.set_progress_bar_config(disable=_snake_case				)

          __lowercase		:			Tuple	    =       '''A red cat sitting on a park bench'''

          __lowercase		:			int	    =       np.random.RandomState(0				)
          __lowercase		:			int	    =       pipe(
              prompt=_snake_case				,       image=_snake_case				,       mask_image=_snake_case				,       strength=0.75				,       guidance_scale=7.5				,       num_inference_steps=15				,       generator=_snake_case				,       output_type='''np'''				,       )

          __lowercase		:			Dict	    =       output.images[0]

          assert image.shape == (512, 512, 3)
          assert np.abs(expected_image - image				).max() < 1E-2


