def SCREAMING_SNAKE_CASE			(       lowercase_:		Dict ):
       if len(__UpperCamelCase ) == 0 or not all(len(__UpperCamelCase ) == 2 for pair in coordinates ):
              raise ValueError('The program cannot work out a fitting polynomial.' )

       if len({tuple(__UpperCamelCase ) for pair in coordinates} ) != len(__UpperCamelCase ):
              raise ValueError('The program cannot work out a fitting polynomial.' )

       _UpperCamelCase       :    Optional[Any]					  =					{x for x, _ in coordinates}
       if len(__UpperCamelCase ) == 1:
              return F"x={coordinates[0][0]}"

       if len(__UpperCamelCase ) != len(__UpperCamelCase ):
              raise ValueError('The program cannot work out a fitting polynomial.' )

       _UpperCamelCase       :    Optional[Any]					  =					len(__UpperCamelCase )

       _UpperCamelCase       :    Optional[int]					  =					0
       _UpperCamelCase       :    List[Any]					  =					[]
       # put the x and x to the power values in a matrix
       while count_of_line < x:
              _UpperCamelCase       :    Dict					  =					0
              _UpperCamelCase       :    Dict					  =					coordinates[count_of_line][0]
              _UpperCamelCase       :    str					  =					[]
              while count_in_line < x:
                     count_line.append(a ** (x - (count_in_line + 1)) )
                     count_in_line += 1
              matrix.append(__UpperCamelCase )
              count_of_line += 1

       _UpperCamelCase       :    Tuple					  =					0
       # put the y values into a vector
       _UpperCamelCase       :    Optional[int]					  =					[]
       while count_of_line < x:
              vector.append(coordinates[count_of_line][1] )
              count_of_line += 1

       _UpperCamelCase       :    str					  =					0

       while count < x:
              _UpperCamelCase       :    Any					  =					0
              while zahlen < x:
                     if count == zahlen:
                            zahlen += 1
                     if zahlen == x:
                            break
                     _UpperCamelCase       :    Union[str, Any]					  =					matrix[zahlen][count] / matrix[count][count]
                     for counting_columns, item in enumerate(matrix[count] ):
                            # manipulating all the values in the matrix
                            matrix[zahlen][counting_columns] -= item * bruch
                     # manipulating the values in the vector
                     vector[zahlen] -= vector[count] * bruch
                     zahlen += 1
              count += 1

       _UpperCamelCase       :    Any					  =					0
       # make solutions
       _UpperCamelCase       :    Optional[int]					  =					[]
       while count < x:
              solution.append(str(vector[count] / matrix[count][count] ) )
              count += 1

       _UpperCamelCase       :    Dict					  =					0
       _UpperCamelCase       :    Dict					  =					'f(x)='

       while count < x:
              _UpperCamelCase       :    Optional[int]					  =					solution[count].split('E' )
              if len(__UpperCamelCase ) > 1:
                     _UpperCamelCase       :    List[str]					  =					F"{remove_e[0]}*10^{remove_e[1]}"
              solved += F"x^{x - (count + 1)}*{solution[count]}"
              if count + 1 != x:
                     solved += "+"
              count += 1

       return solved


if __name__ == "__main__":
 print(points_to_polynomial([]))
 print(points_to_polynomial([[]]))
 print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
 print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
 print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
 print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
 print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
 print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
 print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
 print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))




import gc
import tempfile
import unittest

import numpy as np
import torch

from diffusers import VersatileDiffusionDualGuidedPipeline
from diffusers.utils.testing_utils import load_image, nightly, require_torch_gpu, torch_device


UpperCAmelCase     						=			False




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



 '''simple docstring'''

 def    __snake_case   (     self    :						Optional[Any]					)	->							str:
        # clean up the VRAM after each test
        super().tearDown()
        gc.collect()
        torch.cuda.empty_cache()

 def    __snake_case   (     self    :						Dict					)	->							str:
        _UpperCamelCase       :    Dict					  =					VersatileDiffusionDualGuidedPipeline.from_pretrained('shi-labs/versatile-diffusion'					)
        # remove text_unet
        pipe.remove_unused_weights()
        pipe.to(lowerCamelCase					)
        pipe.set_progress_bar_config(disable=lowerCamelCase					)

        _UpperCamelCase       :    Dict					  =					load_image(
            'https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/versatile_diffusion/benz.jpg'					)

        _UpperCamelCase       :    Optional[int]					  =					torch.manual_seed(0					)
        _UpperCamelCase       :    Optional[Any]					  =					pipe(
            prompt='first prompt'    ,     image=lowerCamelCase    ,     text_to_image_strength=0.7_5    ,     generator=lowerCamelCase    ,     guidance_scale=7.5    ,     num_inference_steps=2    ,     output_type='numpy'    ,     ).images

        with tempfile.TemporaryDirectory() as tmpdirname:
               pipe.save_pretrained(lowerCamelCase					)
               _UpperCamelCase       :    int					  =					VersatileDiffusionDualGuidedPipeline.from_pretrained(lowerCamelCase					)

        pipe.to(lowerCamelCase					)
        pipe.set_progress_bar_config(disable=lowerCamelCase					)

        _UpperCamelCase       :    str					  =					generator.manual_seed(0					)
        _UpperCamelCase       :    Tuple					  =					pipe(
            prompt='first prompt'    ,     image=lowerCamelCase    ,     text_to_image_strength=0.7_5    ,     generator=lowerCamelCase    ,     guidance_scale=7.5    ,     num_inference_steps=2    ,     output_type='numpy'    ,     ).images

        assert np.abs(image - new_image					).sum() < 1e-5, "Models don't have the same forward pass"

 def    __snake_case   (     self    :						Tuple					)	->							Optional[int]:
        _UpperCamelCase       :    Optional[Any]					  =					VersatileDiffusionDualGuidedPipeline.from_pretrained('shi-labs/versatile-diffusion'					)
        pipe.remove_unused_weights()
        pipe.to(lowerCamelCase					)
        pipe.set_progress_bar_config(disable=lowerCamelCase					)

        _UpperCamelCase       :    Union[str, Any]					  =					'cyberpunk 2077'
        _UpperCamelCase       :    str					  =					load_image(
            'https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/versatile_diffusion/benz.jpg'					)
        _UpperCamelCase       :    List[Any]					  =					torch.manual_seed(0					)
        _UpperCamelCase       :    Optional[Any]					  =					pipe(
            prompt=lowerCamelCase    ,     image=lowerCamelCase    ,     text_to_image_strength=0.7_5    ,     generator=lowerCamelCase    ,     guidance_scale=7.5    ,     num_inference_steps=5_0    ,     output_type='numpy'    ,     ).images

        _UpperCamelCase       :    Any					  =					image[0, 2_5_3:2_5_6, 2_5_3:2_5_6, -1]

        assert image.shape == (1, 5_1_2, 5_1_2, 3)
        _UpperCamelCase       :    Optional[int]					  =					np.array([0.0_7_8_7, 0.0_8_4_9, 0.0_8_2_6, 0.0_8_1_2, 0.0_8_0_7, 0.0_7_9_5, 0.0_8_1_8, 0.0_7_9_8, 0.0_7_7_9]					)

        assert np.abs(image_slice.flatten() - expected_slice					).max() < 1e-2



