
def       A       (					lowercase )   ->  bool:
		'''simple docstring'''

		UpperCamelCase		=     (1 + 24 * n) ** 0.5
		return ((1 + root) / 6) % 1 == 0


def       A       (					lowercase = 5_000 )   ->  int:
		'''simple docstring'''

		UpperCamelCase		=     [(i * (3 * i - 1)) // 2 for i in range(1    ,       lowercase )]
		for i, pentagonal_i in enumerate(lowercase ):
				for j in range(lowercase    ,       len(lowercase ) ):
						UpperCamelCase		=     pentagonal_nums[j]
						UpperCamelCase		=     pentagonal_i + pentagonal_j
						UpperCamelCase		=     pentagonal_j - pentagonal_i
						if is_pentagonal(lowercase ) and is_pentagonal(lowercase ):
								return b

		return -1


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


import gc
import unittest

import numpy as np
import torch

from diffusers import StableDiffusionKDiffusionPipeline
from diffusers.utils import slow, torch_device
from diffusers.utils.testing_utils import enable_full_determinism, require_torch_gpu


enable_full_determinism()


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



		def __UpperCamelCase ( self       )  ->					Dict:
				"""simple docstring"""
				# clean up the VRAM after each test
				super().tearDown()
				gc.collect()
				torch.cuda.empty_cache()



		def __UpperCamelCase ( self       )  ->					str:
				"""simple docstring"""
				UpperCamelCase		=     StableDiffusionKDiffusionPipeline.from_pretrained('CompVis/stable-diffusion-v1-4'       )
				UpperCamelCase		=     sd_pipe.to(A_       )
				sd_pipe.set_progress_bar_config(disable=A_       )

				sd_pipe.set_scheduler('sample_euler'       )

				UpperCamelCase		=     'A painting of a squirrel eating a burger'
				UpperCamelCase		=     torch.manual_seed(0       )
				UpperCamelCase		=     sd_pipe([prompt]				,      generator=A_				,      guidance_scale=9.0				,      num_inference_steps=20				,      output_type='np'       )

				UpperCamelCase		=     output.images

				UpperCamelCase		=     image[0, -3:, -3:, -1]

				assert image.shape == (1, 512, 512, 3)
				UpperCamelCase		=     np.array([0.0447, 0.0492, 0.0468, 0.0408, 0.0383, 0.0408, 0.0354, 0.0380, 0.0339]       )

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



		def __UpperCamelCase ( self       )  ->					Any:
				"""simple docstring"""
				UpperCamelCase		=     StableDiffusionKDiffusionPipeline.from_pretrained('stabilityai/stable-diffusion-2-1-base'       )
				UpperCamelCase		=     sd_pipe.to(A_       )
				sd_pipe.set_progress_bar_config(disable=A_       )

				sd_pipe.set_scheduler('sample_euler'       )

				UpperCamelCase		=     'A painting of a squirrel eating a burger'
				UpperCamelCase		=     torch.manual_seed(0       )
				UpperCamelCase		=     sd_pipe([prompt]				,      generator=A_				,      guidance_scale=9.0				,      num_inference_steps=20				,      output_type='np'       )

				UpperCamelCase		=     output.images

				UpperCamelCase		=     image[0, -3:, -3:, -1]

				assert image.shape == (1, 512, 512, 3)
				UpperCamelCase		=     np.array([0.1237, 0.1320, 0.1438, 0.1359, 0.1390, 0.1132, 0.1277, 0.1175, 0.1112]       )

				assert np.abs(image_slice.flatten() - expected_slice       ).max() < 5e-1



		def __UpperCamelCase ( self       )  ->					Optional[int]:
				"""simple docstring"""
				UpperCamelCase		=     StableDiffusionKDiffusionPipeline.from_pretrained('stabilityai/stable-diffusion-2-1-base'       )
				UpperCamelCase		=     sd_pipe.to(A_       )
				sd_pipe.set_progress_bar_config(disable=A_       )

				sd_pipe.set_scheduler('sample_dpmpp_2m'       )

				UpperCamelCase		=     'A painting of a squirrel eating a burger'
				UpperCamelCase		=     torch.manual_seed(0       )
				UpperCamelCase		=     sd_pipe(
				    [prompt]				,      generator=A_				,      guidance_scale=7.5				,      num_inference_steps=15				,      output_type='np'				,      use_karras_sigmas=A_				,      )

				UpperCamelCase		=     output.images

				UpperCamelCase		=     image[0, -3:, -3:, -1]

				assert image.shape == (1, 512, 512, 3)
				UpperCamelCase		=     np.array(
				    [0.1138_1689, 0.1211_2921, 0.138_9457, 0.1254_9606, 0.124_4964, 0.1083_1517, 0.1156_2866, 0.1086_7816, 0.1049_9048]       )

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