"""simple docstring"""







import itertools




def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				int = 1000000						)    ->     Tuple:







     '''simple docstring'''


     __A					:					Any								=		[1]

     for i in itertools.count(len(__UpperCamelCase						)						):
          __A					:					Tuple								=		0
          for j in itertools.count(1						):
               __A					:					Tuple								=		-1 if j % 2 == 0 else +1
               __A					:					Tuple								=		(j * j * 3 - j) // 2
               if index > i:
                    break
               item += partitions[i - index] * sign
               item %= number
               index += j
               if index > i:
                    break
               item += partitions[i - index] * sign
               item %= number

          if item == 0:
               return i
          partitions.append(__UpperCamelCase						)

     return 0


if __name__ == "__main__":
       import doctest

       doctest.testmod()

       print(F'{solution() = }')




"""simple docstring"""

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


__lowercase    =				False






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



						"""simple docstring"""




						def   UpperCAmelCase_ (				self							:    List[str]				)				->				List[Any]:
													'''simple docstring'''



													super().tearDown()
													gc.collect()
													torch.cuda.empty_cache()





						def   UpperCAmelCase_ (				self							:    List[Any]				)				->				List[Any]:
													'''simple docstring'''



													__UpperCamelCase							=VersatileDiffusionDualGuidedPipeline.from_pretrained('''shi-labs/versatile-diffusion'''				)
													# remove text_unet
													pipe.remove_unused_weights()
													pipe.to(UpperCamelCase__				)
													pipe.set_progress_bar_config(disable=UpperCamelCase__				)

													__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(
													    prompt='''first prompt'''     , image=UpperCamelCase__     , text_to_image_strength=0.75     , generator=UpperCamelCase__     , guidance_scale=7.5     , num_inference_steps=2     , output_type='''numpy'''     , ).images

													with tempfile.TemporaryDirectory() as tmpdirname:
																				pipe.save_pretrained(UpperCamelCase__				)
																				__UpperCamelCase							=VersatileDiffusionDualGuidedPipeline.from_pretrained(UpperCamelCase__				)

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

													__UpperCamelCase							=generator.manual_seed(0				)
													__UpperCamelCase							=pipe(
													    prompt='''first prompt'''     , image=UpperCamelCase__     , text_to_image_strength=0.75     , generator=UpperCamelCase__     , 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   UpperCAmelCase_ (				self							:    Optional[int]				)				->				Optional[int]:
													'''simple docstring'''



													__UpperCamelCase							=VersatileDiffusionDualGuidedPipeline.from_pretrained('''shi-labs/versatile-diffusion'''				)
													pipe.remove_unused_weights()
													pipe.to(UpperCamelCase__				)
													pipe.set_progress_bar_config(disable=UpperCamelCase__				)

													__UpperCamelCase							='''cyberpunk 2077'''
													__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(
													    prompt=UpperCamelCase__     , image=UpperCamelCase__     , text_to_image_strength=0.75     , generator=UpperCamelCase__     , 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([0.07_87, 0.08_49, 0.08_26, 0.08_12, 0.08_07, 0.07_95, 0.08_18, 0.07_98, 0.07_79]				)

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



