"""simple docstring"""






import math



def 						a_		(      lowerCamelCase ):

				if not isinstance(lowerCamelCase      ,    lowerCamelCase ):
								UpperCAmelCase__    =							f'''Input value of [number={number}] must be an integer'''
								raise TypeError(lowerCamelCase )

				if number < 1:
								UpperCAmelCase__    =							f'''Input value of [number={number}] must be > 0'''
								raise ValueError(lowerCamelCase )
				elif number == 1:
								return 3
				elif number == 2:
								return 5
				else:
								UpperCAmelCase__    =							int(math.log(number // 3      ,    2 ) ) + 2

								UpperCAmelCase__    =							[3, 5]
								UpperCAmelCase__    =							2
								UpperCAmelCase__    =							3
								for block in range(1      ,    lowerCamelCase ):
												for _ in range(lowerCamelCase ):
																proth_list.append(2 ** (block + 1) + proth_list[proth_index - 1] )
																proth_index += 1
												increment *= 2

				return proth_list[number - 1]


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						for number in range(11):
												lowerCAmelCase__						:						Tuple		  =			0
												try:
																		lowerCAmelCase__						:						Any		  =			proth(number)
												except ValueError:
																		print(F"""ValueError: there is no {number}th Proth number""")
																		continue

												print(F"""The {number}th Proth number: {value}""")




"""simple docstring"""






import unittest

import numpy as np
import torch

from diffusers import VersatileDiffusionImageVariationPipeline
from diffusers.utils.testing_utils import load_image, require_torch_gpu, slow, torch_device


lowerCAmelCase__						:						Optional[int]		  =			False
class        snake_case (				unittest.TestCase       ):




					"""simple docstring"""

					pass






@slow
@require_torch_gpu
class        snake_case (				unittest.TestCase       ):




					"""simple docstring"""

					def 	__lowerCAmelCase		(       self     :			Tuple    ):
									UpperCAmelCase__    =							VersatileDiffusionImageVariationPipeline.from_pretrained('shi-labs/versatile-diffusion'    )
									pipe.to(lowerCamelCase__    )
									pipe.set_progress_bar_config(disable=lowerCamelCase__    )

									UpperCAmelCase__    =							load_image(
									    'https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/versatile_diffusion/benz.jpg'    )
									UpperCAmelCase__    =							torch.manual_seed(0    )
									UpperCAmelCase__    =							pipe(
									    image=lowerCamelCase__					,generator=lowerCamelCase__					,guidance_scale=7.5					,num_inference_steps=50					,output_type='numpy'					,).images

									UpperCAmelCase__    =							image[0, 253:256, 253:256, -1]

									assert image.shape == (1, 512, 512, 3)
									UpperCAmelCase__    =							np.array([0.0_4_4_1, 0.0_4_6_9, 0.0_5_0_7, 0.0_5_7_5, 0.0_6_3_2, 0.0_6_5_0, 0.0_8_6_5, 0.0_9_0_9, 0.0_9_4_5]    )

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



